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

2.
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

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 1687-0247, 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

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

Letters in mathematical physics, ISSN 1573-0530, 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

Compositio mathematica, ISSN 0010-437X, 01/2011, 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 1095-0753, 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

Applied Categorical Structures, ISSN 0927-2852, 8/2017, Volume 25, Issue 4, pp. 505 - 538

This paper establishes a procedure that splits the operations in any algebraic operad, generalizing previous notions of splitting algebraic structures, from...

Dendriform algebra | Rota-Baxter operator | Mathematics | Theory of Computation | L ∞ $L_{\infty }$ algebra | Pre-Lie algebra | Geometry | Successor | A ∞ $A_{\infty }$ algebra | Splitting | Convex and Discrete Geometry | Operad | n -algebra | Mathematical Logic and Foundations | n-algebra | algebra | LIE-ALGEBRAS | MATHEMATICS | PRODUCTS | A(infinity) algebra | L-infinity algebra | Computer science | Algebra

Dendriform algebra | Rota-Baxter operator | Mathematics | Theory of Computation | L ∞ $L_{\infty }$ algebra | Pre-Lie algebra | Geometry | Successor | A ∞ $A_{\infty }$ algebra | Splitting | Convex and Discrete Geometry | Operad | n -algebra | Mathematical Logic and Foundations | n-algebra | algebra | LIE-ALGEBRAS | MATHEMATICS | PRODUCTS | A(infinity) algebra | L-infinity algebra | Computer science | Algebra

Journal Article

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

International Mathematics Research Notices, ISSN 1073-7928, 2013, Volume 2013, Issue 16, pp. 3678 - 3721

We construct a model for the string group as an infinite-dimensional Lie group. In a second step, we extend this model by a contractible Lie group to a Lie...

DIMENSIONAL LIE-GROUPS | MATHEMATICS | PRINCIPAL BUNDLES | UNIVERSAL COMPLEXIFICATIONS | STACKS | 2-GROUPS | L-INFINITY-ALGEBRAS | NON-ABELIAN EXTENSIONS

DIMENSIONAL LIE-GROUPS | MATHEMATICS | PRINCIPAL BUNDLES | UNIVERSAL COMPLEXIFICATIONS | STACKS | 2-GROUPS | L-INFINITY-ALGEBRAS | NON-ABELIAN EXTENSIONS

Journal Article

Applied Categorical Structures, ISSN 0927-2852, 12/2016, Volume 24, Issue 6, pp. 845 - 873

For a Koszul operad 𝒫 $\mathcal {P}$ , there are several existing approaches to the notion of a homotopy between homotopy morphisms of homotopy 𝒫 $\mathcal...

Geometry | Homotopy morphisms | 18D50 | Convex and Discrete Geometry | Homotopy algebras | Models for operads | Mathematics | Theory of Computation | 18G55 | Mathematical Logic and Foundations | OPERADS | MATHEMATICS | MODELS | CATEGORY | DEFORMATIONS | L-INFINITY-ALGEBRAS | Analysis | Algebra | Computer Science

Geometry | Homotopy morphisms | 18D50 | Convex and Discrete Geometry | Homotopy algebras | Models for operads | Mathematics | Theory of Computation | 18G55 | Mathematical Logic and Foundations | OPERADS | MATHEMATICS | MODELS | CATEGORY | DEFORMATIONS | L-INFINITY-ALGEBRAS | Analysis | Algebra | Computer Science

Journal Article

Reviews in Mathematical Physics, ISSN 0129-055X, 07/2016, Volume 28, Issue 6, p. 1650012

We promote geometric prequantization to higher geometry (higher stacks), where a prequantization is given by a higher principal connection (a higher gerbe with...

Geometric quantization | higher differential geometry | FIVEBRANE STRUCTURES | SYMPLECTIC GROUPOIDS | BUNDLE GERBES | ONE-LOOP TEST | CHERN-SIMONS | QUANTUM-FIELD THEORY | COURANT ALGEBROIDS | PHYSICS, MATHEMATICAL | L-INFINITY-ALGEBRAS | QUANTIZATION | D-BRANES

Geometric quantization | higher differential geometry | FIVEBRANE STRUCTURES | SYMPLECTIC GROUPOIDS | BUNDLE GERBES | ONE-LOOP TEST | CHERN-SIMONS | QUANTUM-FIELD THEORY | COURANT ALGEBROIDS | PHYSICS, MATHEMATICAL | L-INFINITY-ALGEBRAS | QUANTIZATION | D-BRANES

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 11/2015, Volume 97, pp. 119 - 132

Given a Lie group acting on a manifold M preserving a closed n+1-form ω, the notion of homotopy moment map for this action was introduced in Fregier (0000), in...

N-plectic geometry | Lie algebras up to homotopy | Homotopy moment maps | FORMS | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL | L-INFINITY-ALGEBRAS | Algebra | Mathematics

N-plectic geometry | Lie algebras up to homotopy | Homotopy moment maps | FORMS | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL | L-INFINITY-ALGEBRAS | Algebra | Mathematics

Journal Article

INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, ISSN 0219-8878, 01/2015, Volume 12, Issue 1, pp. 1550010 - 1-1550010-13

In this paper, we introduce the notion of a (p, k)-Dirac structure in TM circle plus Lambda T-p*M, where 0 <= k <= p - 1. The (p, 0)-Dirac structures are...

(p, k)-Dirac structures | Higher analogues of Courant algebroids | PHYSICS, MATHEMATICAL | L-INFINITY-ALGEBRAS | Nambu-Dirac structures | GEOMETRY | Manifolds

(p, k)-Dirac structures | Higher analogues of Courant algebroids | PHYSICS, MATHEMATICAL | L-INFINITY-ALGEBRAS | Nambu-Dirac structures | GEOMETRY | Manifolds

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 4/2013, Volume 273, Issue 3, pp. 981 - 997

We describe the rational homotopy type of any component of the based mapping space map*(X,Y) as an explicit L ∞ algebra defined on the (desuspended and...

Mapping space | Secondary 54C35 | Rational homotopy | Mathematics, general | Mathematics | Primary 55P62 | L ∞ -algebras | algebras | MATHEMATICS | LIE-ALGEBRA | MODELS | L infinity-algebras | Analysis | Algebra

Mapping space | Secondary 54C35 | Rational homotopy | Mathematics, general | Mathematics | Primary 55P62 | L ∞ -algebras | algebras | MATHEMATICS | LIE-ALGEBRA | MODELS | L infinity-algebras | Analysis | Algebra

Journal Article

Differential Geometry and its Applications, ISSN 0926-2245, 10/2016, Volume 48, pp. 72 - 86

We present the notion of higher Kirillov brackets on the sections of an even line bundle over a supermanifold. When the line bundle is trivial we shall speak...

[formula omitted]-algebroids | Homotopy Poisson algebras | Kirillov structures | [formula omitted]-algebras | Homotopy BV-algebras | algebras | algebroids | MATHEMATICS | BRACKETS | MATHEMATICS, APPLIED | ALGEBRAS | REDUCTION | L-infinity-algebroids | MANIFOLDS | L-infinity-algebras | Algebra

[formula omitted]-algebroids | Homotopy Poisson algebras | Kirillov structures | [formula omitted]-algebras | Homotopy BV-algebras | algebras | algebroids | MATHEMATICS | BRACKETS | MATHEMATICS, APPLIED | ALGEBRAS | REDUCTION | L-infinity-algebroids | MANIFOLDS | L-infinity-algebras | Algebra

Journal Article

International Journal of Geometric Methods in Modern Physics, ISSN 0219-8878, 03/2016, Volume 13, Issue 3

First we show that, associated to any Poisson vector field E on a Poisson manifold (M, pi), there is a canonical Lie algebroid structure on the first jet...

L ∞-Algebra | Lie groupoid | cosymplectic structure | matched pair of Lie algebroids | Poisson structure | Atiyah class | Lichnerowicz-Poisson cohomology | TOPOLOGY | PHYSICS, MATHEMATICAL | JACOBI | LIE ALGEBROIDS | GROUPOIDS | L-infinity-algebra | MATCHED PAIRS

L ∞-Algebra | Lie groupoid | cosymplectic structure | matched pair of Lie algebroids | Poisson structure | Atiyah class | Lichnerowicz-Poisson cohomology | TOPOLOGY | PHYSICS, MATHEMATICAL | JACOBI | LIE ALGEBROIDS | GROUPOIDS | L-infinity-algebra | MATCHED PAIRS

Journal Article

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