Advances in Mathematics, ISSN 0001-8708, 03/2013, Volume 236, pp. 60 - 91

We develop a homotopy theory of L∞ algebras based on the Lawrence–Sullivan construction, a complete differential graded Lie algebra which, as we show,...

Rational homotopy theory | [formula omitted]-algebras | Algebraic models of non-connected spaces | Maurer–Cartan set | algebras | Maurer-Cartan set | Analysis | Models | Algebra

Rational homotopy theory | [formula omitted]-algebras | Algebraic models of non-connected spaces | Maurer–Cartan set | algebras | Maurer-Cartan set | Analysis | Models | Algebra

Journal Article

Operator Theory: Advances and Applications, ISSN 0255-0156, 2018, Volume 267, pp. 167 - 183

Journal Article

Foundations of Computational Mathematics, ISSN 1615-3375, 2/2018, Volume 18, Issue 1, pp. 181 - 247

In this paper, we develop the theory of the discrete moving frame in two different ways. In the first half of the paper, we consider a discrete moving frame...

Discrete integrable systems | 53A55 | Discrete invariants | Finite difference calculus of variations | 53C99 | Multispace | Linear and Multilinear Algebras, Matrix Theory | Mathematics | 14H70 | Numerical Analysis | Local and global syzygies of invariants | 17B80 | Discrete and smooth Maurer–Cartan invariants | Applications of Mathematics | Math Applications in Computer Science | Computer Science, general | Discrete moving frame | 49M25 | Economics, general | 58A40 | MATHEMATICS, APPLIED | POLYNOMIAL INTERPOLATION | EVOLUTION-EQUATIONS | CURVES | Discrete and smooth Maurer-Cartan invariants | MATHEMATICS | SEMISIMPLE HOMOGENEOUS MANIFOLDS | SYMMETRY | INTEGRABLE SYSTEMS | LIE GROUP ACTION | DIFFERENTIAL INVARIANTS | NUMERICAL SCHEMES | COMPUTER SCIENCE, THEORY & METHODS | SURFACES | Bundling | Coalescing | Frames | Interpolation | Lattices | Manifolds (mathematics) | Calculus of variations

Discrete integrable systems | 53A55 | Discrete invariants | Finite difference calculus of variations | 53C99 | Multispace | Linear and Multilinear Algebras, Matrix Theory | Mathematics | 14H70 | Numerical Analysis | Local and global syzygies of invariants | 17B80 | Discrete and smooth Maurer–Cartan invariants | Applications of Mathematics | Math Applications in Computer Science | Computer Science, general | Discrete moving frame | 49M25 | Economics, general | 58A40 | MATHEMATICS, APPLIED | POLYNOMIAL INTERPOLATION | EVOLUTION-EQUATIONS | CURVES | Discrete and smooth Maurer-Cartan invariants | MATHEMATICS | SEMISIMPLE HOMOGENEOUS MANIFOLDS | SYMMETRY | INTEGRABLE SYSTEMS | LIE GROUP ACTION | DIFFERENTIAL INVARIANTS | NUMERICAL SCHEMES | COMPUTER SCIENCE, THEORY & METHODS | SURFACES | Bundling | Coalescing | Frames | Interpolation | Lattices | Manifolds (mathematics) | Calculus of variations

Journal Article

Journal of Noncommutative Geometry, ISSN 1661-6952, 2016, Volume 10, Issue 2, pp. 579 - 661

We connect the homotopy type of simplicial moduli spaces of algebraic structures to the cohomology of their deformation complexes. Then we prove that under...

Homotopical algebra | Props | Derived algebraic geometry | Bialgebras | Deformation theory | Maurer-Cartan simplicial sets | MATHEMATICS, APPLIED | homotopical algebra | REPRESENTATIONS | deformation theory | SPACES | RESOLUTION | GRAPH COMPLEXES | LIE THEORY | MODEL | PHYSICS, MATHEMATICAL | HOMOTOPY-INVARIANCE | bialgebras | MATHEMATICS | derived algebraic geometry | QUANTIZATION | GEOMETRY

Homotopical algebra | Props | Derived algebraic geometry | Bialgebras | Deformation theory | Maurer-Cartan simplicial sets | MATHEMATICS, APPLIED | homotopical algebra | REPRESENTATIONS | deformation theory | SPACES | RESOLUTION | GRAPH COMPLEXES | LIE THEORY | MODEL | PHYSICS, MATHEMATICAL | HOMOTOPY-INVARIANCE | bialgebras | MATHEMATICS | derived algebraic geometry | QUANTIZATION | GEOMETRY

Journal Article

Advances in Mathematics, ISSN 0001-8708, 10/2015, Volume 283, pp. 303 - 361

We construct two algebraic versions of homotopy theory of rational disconnected topological spaces, one based on differential graded commutative associative...

Rational homotopy theory | Maurer–Cartan simplicial set | Differential graded Lie algebra | Koszul duality | Closed model category | Maurer-Cartan simplicial set | MATHEMATICS | ALGEBRAS | Roszul duality | MODELS | Algebra

Rational homotopy theory | Maurer–Cartan simplicial set | Differential graded Lie algebra | Koszul duality | Closed model category | Maurer-Cartan simplicial set | MATHEMATICS | ALGEBRAS | Roszul duality | MODELS | Algebra

Journal Article

Journal of Topology and Analysis, ISSN 1793-5253, 09/2009, Volume 1, Issue 3, pp. 289 - 306

... C*-algebra, the projective resolvent set P-c(A) := C-n \ P(A) is shown to be a disjoint union of domains of holomorphy. B-valued 1-form A(-1)(z)dA(z...

Banach algebra | de Rham cohomology | domain of holomorphy | projective spectrum | maximal ideal space | projective resolvent set | union of hyperplanes | invariant multilinear functional | Maurer-Cartan form | MATHEMATICS

Banach algebra | de Rham cohomology | domain of holomorphy | projective spectrum | maximal ideal space | projective resolvent set | union of hyperplanes | invariant multilinear functional | Maurer-Cartan form | MATHEMATICS

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 08/2009, Volume 89, Issue 2, pp. 115 - 130

In this paper we describe a construction which produces classes in compactifications of the moduli space of curves. This construction extends a construction of...

Maurer-Cartan set | algebra | Moduli space of curves | Noncommutative geometry | Deformation theory | deformation theory | noncommutative geometry | moduli space of curves | PHYSICS, MATHEMATICAL | DEFORMATION | A(infinity)-algebra | School construction

Maurer-Cartan set | algebra | Moduli space of curves | Noncommutative geometry | Deformation theory | deformation theory | noncommutative geometry | moduli space of curves | PHYSICS, MATHEMATICAL | DEFORMATION | A(infinity)-algebra | School construction

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 11/2013, Volume 265, Issue 9, pp. 1916 - 1933

For a tuple A=(A1,A2,…,An) of elements in a unital algebra B over C, its projective spectrumP(A) or p(A) is the collection of z∈Cn, or respectively z∈Pn−1 such...

Maximal ideal space | Union of hyperplanes | de Rham cohomology | Maurer–Cartan form | Cyclic cohomology | Projective spectrum | Projective resolvent set | Invariant multi-linear functional | De Rham cohomology | Maurer-Cartan form | FUNCTIONAL-CALCULUS | MATHEMATICS | Algebra

Maximal ideal space | Union of hyperplanes | de Rham cohomology | Maurer–Cartan form | Cyclic cohomology | Projective spectrum | Projective resolvent set | Invariant multi-linear functional | De Rham cohomology | Maurer-Cartan form | FUNCTIONAL-CALCULUS | MATHEMATICS | Algebra

Journal Article

Journal of Systems Science and Complexity, ISSN 1009-6124, 4/2013, Volume 26, Issue 2, pp. 281 - 290

The authors construct Maurer-Cartan equation, the generating set of the differential invariant algebra and their syzygies for the symmetry groups of a (2+1...

Lie pseudo-groups | Systems Theory, Control | Mathematics of Computing | (2+1)-dimensional Burgers equation | Operations Research/Decision Theory | Maurer-Cartan equation | Mathematics | moving frame method | Statistics, general | Statistical Physics, Dynamical Systems and Complexity | differential invariants | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MOVING COFRAMES | SYMMETRY GROUPS | ALGORITHMS | CURVES | Algebra | Electric generators

Lie pseudo-groups | Systems Theory, Control | Mathematics of Computing | (2+1)-dimensional Burgers equation | Operations Research/Decision Theory | Maurer-Cartan equation | Mathematics | moving frame method | Statistics, general | Statistical Physics, Dynamical Systems and Complexity | differential invariants | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MOVING COFRAMES | SYMMETRY GROUPS | ALGORITHMS | CURVES | Algebra | Electric generators

Journal Article

ADVANCES IN MATHEMATICS, ISSN 0001-8708, 03/2013, Volume 236, pp. 60 - 91

We develop a homotopy theory of L-infinity algebras based on the Lawrence-Sullivan construction, a complete differential graded Lie algebra which, as we show,...

Rational homotopy theory | MATHEMATICS | Maurer-Cartan set | SECTIONS | Algebraic models of non-connected spaces | L-infinity-algebras | HOMOLOGICAL ALGEBRA | RATIONAL HOMOTOPY | DEFORMATION

Rational homotopy theory | MATHEMATICS | Maurer-Cartan set | SECTIONS | Algebraic models of non-connected spaces | L-infinity-algebras | HOMOLOGICAL ALGEBRA | RATIONAL HOMOTOPY | DEFORMATION

Journal Article

Advances in Mathematics, ISSN 0001-8708, 03/2013, Volume 235, pp. 296 - 320

We set up a formalism of Maurer–Cartan moduli sets for L∞ algebras and associated twistings based on the closed model category structure on formal differential graded algebras (a.k.a...

Maurer–Cartan element | Differential graded algebra | Sullivan model | Chevalley–Eilenberg cohomology | Closed model category | Chevalley-Eilenberg cohomology | Maurer-Cartan element | MATHEMATICS | ALGEBRAS | CYCLIC HOMOLOGY | SECTIONS | RATIONAL HOMOTOPY | Analysis | Algebra

Maurer–Cartan element | Differential graded algebra | Sullivan model | Chevalley–Eilenberg cohomology | Closed model category | Chevalley-Eilenberg cohomology | Maurer-Cartan element | MATHEMATICS | ALGEBRAS | CYCLIC HOMOLOGY | SECTIONS | RATIONAL HOMOTOPY | Analysis | Algebra

Journal Article

02/2017

Algebraic & Geometric Topology, 19(3):1453-1476, 2019 The goal of the present paper is to introduce a smaller, but equivalent version of the...

Journal Article

Canadian mathematical bulletin, ISSN 0008-4395, 09/2017, Volume 60, Issue 3, pp. 470 - 477

.... Similarly, we also have a realization functor fromthe category of complete differential graded Lie algebras to the category of simplicial sets...

Rational homotopy theory | Maurer-Cartan elements | Complete differential graded lie algebra | MATHEMATICS | complete differential graded Lie algebra | RATIONAL HOMOTOPY-THEORY | rational homotopy theory

Rational homotopy theory | Maurer-Cartan elements | Complete differential graded lie algebra | MATHEMATICS | complete differential graded Lie algebra | RATIONAL HOMOTOPY-THEORY | rational homotopy theory

Journal Article

Ce mémoire traite des structures affines et de leur rapport à la géométrie de l'information. Nous y introduisons la notion de T-plongement. Il permet de...

KV-cohomologie | Modèle statistique | T-plongement | Alpha connexion | Maurer-Cartan Polynomial | Left-symmetric algebras | Métrique de Fisher | Fisher metric | Statistics model | Polynôme de Maurer-Cartan

KV-cohomologie | Modèle statistique | T-plongement | Alpha connexion | Maurer-Cartan Polynomial | Left-symmetric algebras | Métrique de Fisher | Fisher metric | Statistics model | Polynôme de Maurer-Cartan

Dissertation

Letters in Mathematical Physics, ISSN 0377-9017, 5/2017, Volume 107, Issue 5, pp. 861 - 885

We study Maurer–Cartan elements on homotopy Poisson manifolds of degree n. They unify many twisted or homotopy structures in Poisson geometry and mathematical...

Theoretical, Mathematical and Computational Physics | Complex Systems | Lie 2-algebras | Physics | Maurer–Cartan elements | 53D17 | Geometry | Symplectic NQ-manifolds | 17B99 | L_\infty $$ L ∞ -algebras | Courant algebroids | Group Theory and Generalizations | Homotopy Poisson manifolds | algebras | BRACKETS | REDUCTION | Maurer-Cartan elements | L-infinity-algebras | PHYSICS, MATHEMATICAL | BIALGEBROIDS | QUASI | GEOMETRY | Algebra

Theoretical, Mathematical and Computational Physics | Complex Systems | Lie 2-algebras | Physics | Maurer–Cartan elements | 53D17 | Geometry | Symplectic NQ-manifolds | 17B99 | L_\infty $$ L ∞ -algebras | Courant algebroids | Group Theory and Generalizations | Homotopy Poisson manifolds | algebras | BRACKETS | REDUCTION | Maurer-Cartan elements | L-infinity-algebras | PHYSICS, MATHEMATICAL | BIALGEBROIDS | QUASI | GEOMETRY | Algebra

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 1/2013, Volume 103, Issue 1, pp. 79 - 112

We give a general treatment of the Maurer–Cartan equation in homotopy algebras and describe the operads and formal differential geometric objects governing the...

Theoretical, Mathematical and Computational Physics | Statistical Physics, Dynamical Systems and Complexity | 16E45 | Physics | Geometry | 17B55 | 17B66 | operad | 18D50 | A-infinity algebra | differential graded Lie algebra | Maurer–Cartan element | Group Theory and Generalizations | L-infinity algebra | twisting | Maurer-Cartan element | OPERADS | DUALITY | PHYSICS, MATHEMATICAL | Algebra

Theoretical, Mathematical and Computational Physics | Statistical Physics, Dynamical Systems and Complexity | 16E45 | Physics | Geometry | 17B55 | 17B66 | operad | 18D50 | A-infinity algebra | differential graded Lie algebra | Maurer–Cartan element | Group Theory and Generalizations | L-infinity algebra | twisting | Maurer-Cartan element | OPERADS | DUALITY | PHYSICS, MATHEMATICAL | Algebra

Journal Article

Bollettino dell'Unione Matematica Italiana, ISSN 1972-6724, 3/2019, Volume 12, Issue 1, pp. 197 - 219

In order to study the deformations of foliations of codimension 1 of a smooth manifold L, de Bartolomeis and Iordan defined the DGLA $$ \mathcal {Z}^{*}\left(...

32E99 | 53C12 | Differential graded Lie Algebras | Levi flat hypersurface | Mathematics, general | 16W25 | Mathematics | Foliations | Maurer–Cartan equation | Primary 32G10 | Graded derivations

32E99 | 53C12 | Differential graded Lie Algebras | Levi flat hypersurface | Mathematics, general | 16W25 | Mathematics | Foliations | Maurer–Cartan equation | Primary 32G10 | Graded derivations

Journal Article

Results in Mathematics, ISSN 1422-6383, 10/2011, Volume 60, Issue 1, pp. 423 - 452

A recursive algorithm for the equivariant method of moving frames, for both finite-dimensional Lie group actions and Lie pseudo-groups, is developed and...

53A55 | 53A15 | Maurer–Cartan form | contact form | Mathematics | invariant differential form | 58H05 | Moving frame | Primary 22F05 | Secondary 53A04 | recurrence formula | Mathematics, general | Lie group | differential invariant | Lie pseudo-group | Maurer-Cartan form | MATHEMATICS, APPLIED | COFRAMES | INVARIANTS | EQUATIONS | ALGORITHMS | LIE PSEUDO-GROUPS | MATHEMATICS | FOUNDATIONS | Algorithms

53A55 | 53A15 | Maurer–Cartan form | contact form | Mathematics | invariant differential form | 58H05 | Moving frame | Primary 22F05 | Secondary 53A04 | recurrence formula | Mathematics, general | Lie group | differential invariant | Lie pseudo-group | Maurer-Cartan form | MATHEMATICS, APPLIED | COFRAMES | INVARIANTS | EQUATIONS | ALGORITHMS | LIE PSEUDO-GROUPS | MATHEMATICS | FOUNDATIONS | Algorithms

Journal Article

Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), ISSN 1815-0659, 2013, Volume 9, p. 029

Given a Lie pseudo-group action, an equivariant moving frame exists in the neighborhood of a submanifold jet provided the action is free and regular. For local...

Differential invariant | Equivalence problem | Maurer-Cartan form | Moving frame | equivalence problem | moving frame | FINITENESS | DIFFERENTIAL INVARIANTS | SYMMETRY GROUPS | EQUATIONS | LIE PSEUDO-GROUPS | PHYSICS, MATHEMATICAL | differential invariant

Differential invariant | Equivalence problem | Maurer-Cartan form | Moving frame | equivalence problem | moving frame | FINITENESS | DIFFERENTIAL INVARIANTS | SYMMETRY GROUPS | EQUATIONS | LIE PSEUDO-GROUPS | PHYSICS, MATHEMATICAL | differential invariant

Journal Article

Selecta Mathematica, ISSN 1022-1824, 11/2005, Volume 11, Issue 1, pp. 99 - 126

This paper begins a series devoted to developing a general and practical theory of moving frames for infinite-dimensional Lie pseudo-groups. In this first,...

structure equations | 58J70 | Maurer–Cartan form | groupoid | 58A15 | Mathematics, general | 58A20 | Mathematics | 58H05 | Lie pseudo-group | Groupoid | Structure equations | Maurer-Cartan form | MATHEMATICS, APPLIED | MOVING COFRAMES | SYMMETRIES | DIFFERENTIAL-EQUATIONS | ALGORITHMS | MATHEMATICS | INVARIANT SIGNATURE CURVES | THEOREMS | SYSTEMS | FOUNDATIONS | TRANSFORMATIONS | GEOMETRY | Algorithms

structure equations | 58J70 | Maurer–Cartan form | groupoid | 58A15 | Mathematics, general | 58A20 | Mathematics | 58H05 | Lie pseudo-group | Groupoid | Structure equations | Maurer-Cartan form | MATHEMATICS, APPLIED | MOVING COFRAMES | SYMMETRIES | DIFFERENTIAL-EQUATIONS | ALGORITHMS | MATHEMATICS | INVARIANT SIGNATURE CURVES | THEOREMS | SYSTEMS | FOUNDATIONS | TRANSFORMATIONS | GEOMETRY | Algorithms

Journal Article

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