Journal of Algebra, ISSN 0021-8693, 05/2015, Volume 430, pp. 260 - 302

In this paper we consider L∞-algebras equipped with complete descending filtrations. We prove that, under some mild conditions, an L∞ quasi-isomorphism U:L→L˜...

Simplicial sets | L-infinity algebras | Algebra

Simplicial sets | L-infinity algebras | Algebra

Journal Article

Compositio Mathematica, ISSN 0010-437X, 09/2015, Volume 151, Issue 9, pp. 1763 - 1790

We consider the problem of deforming simultaneously a pair of given structures. We show that such deformations are governed by an L-infinity-algebra, which we...

generalized complex manifold | deformation | Dirac manifold | Maurer-Cartan equation | Lz-algebra | Poisson manifold | BRACKETS | COISOTROPIC SUBMANIFOLDS | Maurer Cartan equation | BIALGEBROIDS | L-INFINITY-ALGEBRAS | QUASI | LIE-ALGEBRAS | MATHEMATICS | COMPLEX ANALYTIC STRUCTURES | L-infinity-algebra | MANIFOLDS | QUANTIZATION | Geometry | Theoretical mathematics | Construction | Deformation | Brackets | Machinery | Manifolds (mathematics) | Construction equipment

generalized complex manifold | deformation | Dirac manifold | Maurer-Cartan equation | Lz-algebra | Poisson manifold | BRACKETS | COISOTROPIC SUBMANIFOLDS | Maurer Cartan equation | BIALGEBROIDS | L-INFINITY-ALGEBRAS | QUASI | LIE-ALGEBRAS | MATHEMATICS | COMPLEX ANALYTIC STRUCTURES | L-infinity-algebra | MANIFOLDS | QUANTIZATION | Geometry | Theoretical mathematics | Construction | Deformation | Brackets | Machinery | Manifolds (mathematics) | Construction equipment

Journal Article

INTERNATIONAL MATHEMATICS RESEARCH NOTICES, ISSN 1073-7928, 03/2019, Volume 2019, Issue 5, pp. 1503 - 1542

We study higher-order analogues of Dirac structures, extending the multisymplectic structures that arise in field theory. We define higher Dirac structures as...

FORMS | MATHEMATICS | FORMALISM | L-INFINITY-ALGEBRAS | GEOMETRY

FORMS | MATHEMATICS | FORMALISM | L-INFINITY-ALGEBRAS | GEOMETRY

Journal Article

Advances in Mathematics, ISSN 0001-8708, 10/2019, Volume 354, p. 106754

Over a field of characteristic zero, every deformation problem with cohomology constraints is controlled by a pair consisting of a differential graded Lie...

Links | Milnor fibers | Weight filtration | Deformation theory | Fundamental group | L-infinity algebras and modules | TOPOLOGY | MATHEMATICS | SYSTEMS | HOMOTOPY | COHOMOLOGY JUMP LOCI

Links | Milnor fibers | Weight filtration | Deformation theory | Fundamental group | L-infinity algebras and modules | TOPOLOGY | MATHEMATICS | SYSTEMS | HOMOTOPY | COHOMOLOGY JUMP LOCI

Journal Article

5.
Full Text
Mixed Hodge structures and representations of fundamental groups of algebraic varieties

Advances in Mathematics, ISSN 0001-8708, 06/2019, Volume 349, pp. 869 - 910

Given a complex variety X, a linear algebraic group G and a representation ρ of the fundamental group π1(X,x) into G, we develop a framework for constructing a...

Hodge theory | [formula omitted] algebras | Representation varieties | Complex algebraic geometry | Formal deformation theory | Fundamental groups | MATHEMATICS | L-infinity algebras | Algebraic Geometry | Mathematics

Hodge theory | [formula omitted] algebras | Representation varieties | Complex algebraic geometry | Formal deformation theory | Fundamental groups | MATHEMATICS | L-infinity algebras | Algebraic Geometry | Mathematics

Journal Article

Advances in Mathematics, ISSN 0001-8708, 01/2016, Volume 288, pp. 527 - 575

Given a Lie group G, one constructs a principal G-bundle on a manifold X by taking a cover U→X, specifying a transition cocycle on the cover, and descending...

Simplicial manifolds | String 2-group | Bundle gerbes | MATHEMATICS | CATEGORIES | L-INFINITY-ALGEBRAS

Simplicial manifolds | String 2-group | Bundle gerbes | MATHEMATICS | CATEGORIES | L-INFINITY-ALGEBRAS

Journal Article

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, ISSN 1446-7887, 02/2020, Volume 108, Issue 1, pp. 120 - 144

Given a vector field on a manifold M, we define a globally conserved quantity to be a di fferential form whose Lie derivative is exact. Integrals of conserved...

MATHEMATICS | conservation laws | homotopy co-momentum map | L-INFINITY-ALGEBRAS | multisymplectic manifolds | GEOMETRY | Differential Geometry | Mathematics

MATHEMATICS | conservation laws | homotopy co-momentum map | L-INFINITY-ALGEBRAS | multisymplectic manifolds | GEOMETRY | Differential Geometry | Mathematics

Journal Article

Journal of Algebra, ISSN 0021-8693, 09/2015, Volume 438, pp. 90 - 118

We give some formality criteria for a differential graded Lie algebra to be formal. For instance, we show that a DG-Lie algebra L is formal if and only if the...

Differential graded Lie algebras | [formula omitted]-algebras | Spectral sequences | L ∞ -algebras | KAHLER-MANIFOLDS | MATHEMATICS | MODELS | SPACES | OBSTRUCTIONS | L-infinity-algebras | HOMOTOPY-THEORY | DEFORMATION-THEORY | MODULI | Algebra

Differential graded Lie algebras | [formula omitted]-algebras | Spectral sequences | L ∞ -algebras | KAHLER-MANIFOLDS | MATHEMATICS | MODELS | SPACES | OBSTRUCTIONS | L-infinity-algebras | HOMOTOPY-THEORY | DEFORMATION-THEORY | MODULI | Algebra

Journal Article

Journal of High Energy Physics, ISSN 1126-6708, 4/2015, Volume 2015, Issue 4, pp. 1 - 67

We develop semistrict higher gauge theory from first principles. In particular, we describe the differential Deligne cohomology underlying semistrict principal...

Integrable Field Theories | M-Theory | Extended Supersymmetry | Quantum Physics | Differential and Algebraic Geometry | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | LIE-ALGEBRAS | BUNDLE GERBES | TWISTOR SPACE | DIFFERENTIAL GEOMETRY | L-INFINITY-ALGEBRAS | 2-ALGEBRAS | PHYSICS, PARTICLES & FIELDS | Algebra | String theory | Category Theory | Mathematics - Differential Geometry | Mathematical Physics | Nuclear and High Energy Physics | Mathematics - Category Theory | Mathematics | High Energy Physics - Theory

Integrable Field Theories | M-Theory | Extended Supersymmetry | Quantum Physics | Differential and Algebraic Geometry | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | LIE-ALGEBRAS | BUNDLE GERBES | TWISTOR SPACE | DIFFERENTIAL GEOMETRY | L-INFINITY-ALGEBRAS | 2-ALGEBRAS | PHYSICS, PARTICLES & FIELDS | Algebra | String theory | Category Theory | Mathematics - Differential Geometry | Mathematical Physics | Nuclear and High Energy Physics | Mathematics - Category Theory | Mathematics | High Energy Physics - Theory

Journal Article

Applied Categorical Structures, ISSN 0927-2852, 8/2017, Volume 25, Issue 4, pp. 489 - 503

We construct a symmetric monoidal category S Lie ∞ MC ${\mathfrak {S}}\mathsf {Lie}_{\infty }^{\text {MC}}$ whose objects are shifted L ∞ -algebras equipped...

Geometry | Enriched categories | Convex and Discrete Geometry | Mathematics | Theory of Computation | L-infinity algebras | Mathematical Logic and Foundations

Geometry | Enriched categories | Convex and Discrete Geometry | Mathematics | Theory of Computation | L-infinity algebras | Mathematical Logic and Foundations

Journal Article

International Mathematics Research Notices, ISSN 1073-7928, 2013, Volume 2013, Issue 16, pp. 3790 - 3855

We use Chen's iterated integrals to integrate representations up to homotopy. That is, we construct an A(infinity) functor integral : Rep(infinity)(A) -> (R)...

MATHEMATICS | LIE BRACKETS | L-INFINITY-ALGEBRAS | DEFORMATIONS

MATHEMATICS | LIE BRACKETS | L-INFINITY-ALGEBRAS | DEFORMATIONS

Journal Article

JOURNAL OF LIE THEORY, ISSN 0949-5932, 2016, Volume 26, Issue 4, pp. 1037 - 1067

Multisymplectic geometry admits an operation that has no counterpart in symplectic geometry, namely, taking the product of two multisymplectic manifolds...

MATHEMATICS | strong homotopy Lie algebra | moment map | Multisymplectic manifold | L-INFINITY-ALGEBRAS | GEOMETRY

MATHEMATICS | strong homotopy Lie algebra | moment map | Multisymplectic manifold | L-INFINITY-ALGEBRAS | GEOMETRY

Journal Article

Journal of Homotopy and Related Structures, ISSN 2193-8407, 6/2016, Volume 11, Issue 2, pp. 309 - 332

By using homotopy transfer techniques in the context of rational homotopy theory, we show that if $$C$$ C is a coalgebra model of a space $$X$$ X , then the...

Algebra | L_\infty $$ L ∞ -algebra | Functional Analysis | Mapping space | Secondary 54C35 | Algebraic Topology | Rational homotopy | Mathematics | Number Theory | Primary 55P62 | algebra | MATHEMATICS | L-infinity-algebra | LIE-ALGEBRA | HOMOLOGICAL ALGEBRA | WHITEHEAD PRODUCTS | CONE | L-INFINITY-ALGEBRAS | DEFORMATION-THEORY | Mathematics - Algebraic Topology

Algebra | L_\infty $$ L ∞ -algebra | Functional Analysis | Mapping space | Secondary 54C35 | Algebraic Topology | Rational homotopy | Mathematics | Number Theory | Primary 55P62 | algebra | MATHEMATICS | L-infinity-algebra | LIE-ALGEBRA | HOMOLOGICAL ALGEBRA | WHITEHEAD PRODUCTS | CONE | L-INFINITY-ALGEBRAS | DEFORMATION-THEORY | Mathematics - Algebraic Topology

Journal Article

Communications in Contemporary Mathematics, ISSN 0219-1997, 06/2017, Volume 19, Issue 3, p. 1650034

We study the extension of a Lie algebroid by a representation up to homotopy, including semidirect products of a Lie algebroid with such representations. The...

Representation up to homotopy | integration | Lie 2-groupoids | Courant algebroids | Lie 2-algebroids | BRACKETS | MATHEMATICS, APPLIED | REPRESENTATIONS | HOMOTOPY | L-INFINITY-ALGEBRAS | MATHEMATICS | GROUPOIDS | GEOMETRY

Representation up to homotopy | integration | Lie 2-groupoids | Courant algebroids | Lie 2-algebroids | BRACKETS | MATHEMATICS, APPLIED | REPRESENTATIONS | HOMOTOPY | L-INFINITY-ALGEBRAS | MATHEMATICS | GROUPOIDS | GEOMETRY

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 12/2014, Volume 86, pp. 497 - 533

We disclose the mathematical structure underlying the gauge field sector of the recently constructed non-abelian superconformal models in six space–time...

Superconformal models | [formula omitted]-manifolds | Tensor hierarchy | [formula omitted]-infinity algebras | Q-manifolds | L-infinity algebras | MATHEMATICS | GAUGE ALGEBRA | POISSON SIGMA-MODELS | PHYSICS, MATHEMATICAL | Analysis | Algebra

Superconformal models | [formula omitted]-manifolds | Tensor hierarchy | [formula omitted]-infinity algebras | Q-manifolds | L-infinity algebras | MATHEMATICS | GAUGE ALGEBRA | POISSON SIGMA-MODELS | PHYSICS, MATHEMATICAL | Analysis | Algebra

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 9/2018, Volume 108, Issue 9, pp. 2055 - 2097

We describe some $$L_{\infty }$$ L∞ model for the local period map of a compact Kähler manifold. Applications include the study of deformations with associated...

Geometry | 32G20 | 14D07 | Theoretical, Mathematical and Computational Physics | Complex Systems | Group Theory and Generalizations | Yukawa algebra | L-infinity algebras | 13D10 | Physics | Formal period maps | LIE-ALGEBRAS | SPACE | COHOMOLOGY | DEFORMATIONS | CONSTRUCTION | MANIFOLDS | PHYSICS, MATHEMATICAL | HOMOTOPY-THEORY | GEOMETRY | Analysis | Algebra

Geometry | 32G20 | 14D07 | Theoretical, Mathematical and Computational Physics | Complex Systems | Group Theory and Generalizations | Yukawa algebra | L-infinity algebras | 13D10 | Physics | Formal period maps | LIE-ALGEBRAS | SPACE | COHOMOLOGY | DEFORMATIONS | CONSTRUCTION | MANIFOLDS | PHYSICS, MATHEMATICAL | HOMOTOPY-THEORY | GEOMETRY | Analysis | Algebra

Journal Article

JOURNAL OF NONCOMMUTATIVE GEOMETRY, ISSN 1661-6952, 2019, Volume 13, Issue 1, pp. 297 - 361

Given a differential graded (dg) symmetric Frobenius algebra A we construct an unbounded complex D* (A, A), called the Tate-Hochschild complex, which arises as...

A-infinity algebras | string topology | MATHEMATICS | MATHEMATICS, APPLIED | Tate-Hochschild complex | Frobenius algebras | DUALITY | L-infinity algebras | PHYSICS, MATHEMATICAL | HOMOLOGY

A-infinity algebras | string topology | MATHEMATICS | MATHEMATICS, APPLIED | Tate-Hochschild complex | Frobenius algebras | DUALITY | L-infinity algebras | PHYSICS, MATHEMATICAL | HOMOLOGY

Journal Article

Classical and Quantum Gravity, ISSN 0264-9381, 05/2015, Volume 32, Issue 9, pp. 95005 - 95054

We consider the De Donder-Weyl (DW) Hamiltonian formulation of the Palatini action of vielbein gravity formulated in terms of the solder form and spin...

Geometry | De Donder-Weyl | Palatini gravity | Multisymplectic | Vielbein gravity | GENERAL-RELATIVITY | PHYSICS, MULTIDISCIPLINARY | SPIN STRUCTURES | CLASSICAL FIELD-THEORY | ASHTEKAR VARIABLES | CANONICAL STRUCTURE | GAUGE-NATURAL BUNDLES | L-INFINITY-ALGEBRAS | QUANTIZED-FIELDS | SYMPLECTIC APPROACH | POISSON BRACKET | vielbein gravity | ASTRONOMY & ASTROPHYSICS | multisymplectic geometry | PHYSICS, PARTICLES & FIELDS | Formulations | Gravitation | Construction | Solders | Brackets | Mathematical analysis | Independent variables | Quantum gravity | General Relativity and Quantum Cosmology | Mathematics | Mathematical Physics | Physics

Geometry | De Donder-Weyl | Palatini gravity | Multisymplectic | Vielbein gravity | GENERAL-RELATIVITY | PHYSICS, MULTIDISCIPLINARY | SPIN STRUCTURES | CLASSICAL FIELD-THEORY | ASHTEKAR VARIABLES | CANONICAL STRUCTURE | GAUGE-NATURAL BUNDLES | L-INFINITY-ALGEBRAS | QUANTIZED-FIELDS | SYMPLECTIC APPROACH | POISSON BRACKET | vielbein gravity | ASTRONOMY & ASTROPHYSICS | multisymplectic geometry | PHYSICS, PARTICLES & FIELDS | Formulations | Gravitation | Construction | Solders | Brackets | Mathematical analysis | Independent variables | Quantum gravity | General Relativity and Quantum Cosmology | Mathematics | Mathematical Physics | Physics

Journal Article

Compositio Mathematica, ISSN 0010-437X, 1/2011, Volume 147, Issue 1, pp. 105 - 160

We prove a version of Kontsevich's formality theorem for two subspaces (branes) of a vector space X. The result implies, in particular, that the Kontsevich...

coisotropic submanifolds | Koszul algebras | L-algebras and morphisms | A-bimodules | Koszul duality | deformation quantization | MATHEMATICS | COMPLEX | L-infinity-algebras and morphisms | A(infinity)-bimodules | FORMALITY THEOREM | Quantization | Theorems | Deformation | Vector spaces | Subspaces | Branes | Quantum Algebra | Mathematics | Mathematical Physics | Physics

coisotropic submanifolds | Koszul algebras | L-algebras and morphisms | A-bimodules | Koszul duality | deformation quantization | MATHEMATICS | COMPLEX | L-infinity-algebras and morphisms | A(infinity)-bimodules | FORMALITY THEOREM | Quantization | Theorems | Deformation | Vector spaces | Subspaces | Branes | Quantum Algebra | Mathematics | Mathematical Physics | Physics

Journal Article

Advances in Theoretical and Mathematical Physics, ISSN 1095-0761, 2012, Volume 16, Issue 5, pp. 1485 - 1589

Recent work applying higher gauge theory to the superstring has indicated the presence of "higher symmetry". Infinitesimally, this is realized by a "Lie...

LORENTZ | HIGHER GAUGE-THEORY | BRANES | 2-GROUPS | SPINORS | PHYSICS, MATHEMATICAL | L-INFINITY-ALGEBRAS | OCTONIONS | PHYSICS, PARTICLES & FIELDS

LORENTZ | HIGHER GAUGE-THEORY | BRANES | 2-GROUPS | SPINORS | PHYSICS, MATHEMATICAL | L-INFINITY-ALGEBRAS | OCTONIONS | PHYSICS, PARTICLES & FIELDS

Journal Article

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