Communications in algebra, ISSN 1532-4125, 2012, Volume 40, Issue 6, pp. 2243 - 2260

We identify Čech cocycles in nonabelian (formal) group cohomology with Maurer-Cartan elements in a suitable L ∞ -algebra. Applications to deformation theory...

algebras | Differential graded Lie algebras | Functors of Artin rings | MATHEMATICS | L-infinity-algebras | LIE-ALGEBRA HOMOLOGY

algebras | Differential graded Lie algebras | Functors of Artin rings | MATHEMATICS | L-infinity-algebras | LIE-ALGEBRA HOMOLOGY

Journal Article

Journal of Algebra, ISSN 0021-8693, 02/2017, Volume 472, pp. 437 - 479

We extend the classical characterization of a finite-dimensional Lie algebra g in terms of its Maurer–Cartan algebra—the familiar differential graded algebra...

[formula omitted]-algebra | Sh Lie–Rinehart algebra | Higher homotopies | Foliation | Quasi Lie–Rinehart algebra | Maurer–Cartan algebra | algebra | MATHEMATICS | Maurer-Cartan algebra | Sh Lie-Rinehart algebra | L-infinity-algebra | Quasi Lie-Rinehart algebra | Algebra

[formula omitted]-algebra | Sh Lie–Rinehart algebra | Higher homotopies | Foliation | Quasi Lie–Rinehart algebra | Maurer–Cartan algebra | algebra | MATHEMATICS | Maurer-Cartan algebra | Sh Lie-Rinehart algebra | L-infinity-algebra | Quasi Lie-Rinehart algebra | 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, 12/2015, Volume 98, pp. 340 - 354

We study n-ary commutative superalgebras and L∞-algebras that possess a skew-symmetric invariant form, using the derived bracket formalism. This class of...

[formula omitted]-ary and [formula omitted]-algebras | Lie [formula omitted]-algebras | Invariant form | algebras | Lie n-algebras | N-ary and L | MATHEMATICS | COHOMOLOGY | n-ary and L-infinity-algebras | LIE | PHYSICS, MATHEMATICAL | Algebra

[formula omitted]-ary and [formula omitted]-algebras | Lie [formula omitted]-algebras | Invariant form | algebras | Lie n-algebras | N-ary and L | MATHEMATICS | COHOMOLOGY | n-ary and L-infinity-algebras | LIE | PHYSICS, MATHEMATICAL | Algebra

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, 08/2012, Volume 9, Issue 5, pp. 1250043 - 1250031

The semidirect product of a Lie algebra and a 2-term representation up to homotopy is a Lie 2-algebra. Such Lie 2-algebras include many examples arising from...

butterfly | Representations up to homotopy | integration | algebras | omni-Lie algebras | Lie 2-algebras | crossed modules | COURANT ALGEBROIDS | HOMOTOPY | L-infinity-algebras | PHYSICS, MATHEMATICAL | Lie groups | Representations

butterfly | Representations up to homotopy | integration | algebras | omni-Lie algebras | Lie 2-algebras | crossed modules | COURANT ALGEBROIDS | HOMOTOPY | L-infinity-algebras | PHYSICS, MATHEMATICAL | Lie groups | Representations

Journal Article

JOURNAL OF ALGEBRA, ISSN 0021-8693, 05/2015, Volume 430, pp. 260 - 302

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

Simplicial sets | MATHEMATICS | MANIFOLDS | L-infinity algebras

Simplicial sets | MATHEMATICS | MANIFOLDS | L-infinity algebras

Journal Article

Electronic Research Announcements in Mathematical Sciences, ISSN 1935-9179, 2012, Volume 19, pp. 58 - 76

In this paper, we describe an integration of exact Courant algebroids to symplectic 2-groupoids, and we show that the differentiation procedure from [32]...

Higher structures | Courant algebroids | Lie theory | Poisson geometry | Symplectic geometry | BRACKETS | INTEGRABILITY | poisson geometry | LIE BIALGEBROIDS | HOMOTOPY | symplectic geometry | L-INFINITY-ALGEBRAS | MATHEMATICS | higher structures | GROUPOIDS | POISSON MANIFOLDS

Higher structures | Courant algebroids | Lie theory | Poisson geometry | Symplectic geometry | BRACKETS | INTEGRABILITY | poisson geometry | LIE BIALGEBROIDS | HOMOTOPY | symplectic geometry | L-INFINITY-ALGEBRAS | MATHEMATICS | higher structures | GROUPOIDS | POISSON MANIFOLDS

Journal Article

APPLIED CATEGORICAL STRUCTURES, ISSN 0927-2852, 08/2017, Volume 25, Issue 4, pp. 489 - 503

We construct a symmetric monoidal category whose objects are shifted L (a) -algebras equipped with a complete descending filtration. Morphisms of this category...

MATHEMATICS | Enriched categories | L-infinity algebras

MATHEMATICS | Enriched categories | L-infinity algebras

Journal Article

International Journal of Mathematics, ISSN 0129-167X, 07/2012, Volume 23, Issue 7, pp. 1250053 - 1250030

We identify dglas that control infinitesimal deformations of the pairs (manifold, Higgs bundle) and of Hitchin pairs. As a consequence, we recover known...

algebras | Hitchin pairs | differential graded Lie algebras | Deformation theory | MATHEMATICS | COMPACT KAHLER-MANIFOLDS | L-infinity-algebras | MODULI | Bundling | Manifolds | Descriptions | Obstructions | Deformation | Mathematical analysis | Standards

algebras | Hitchin pairs | differential graded Lie algebras | Deformation theory | MATHEMATICS | COMPACT KAHLER-MANIFOLDS | L-infinity-algebras | MODULI | Bundling | Manifolds | Descriptions | Obstructions | Deformation | Mathematical analysis | Standards

Journal Article

International Mathematics Research Notices, ISSN 1073-7928, 2014, Volume 2014, Issue 9, pp. 2440 - 2493

An NQ-manifold is a nonnegatively graded supermanifold with a degree 1 homological vector field. The focus of this paper is to define the Wilson loops/lines in...

MATHEMATICS | HOMOTOPY | CYCLIC BAR COMPLEX | L-INFINITY-ALGEBRAS | LIE ALGEBROIDS | GROUPOIDS

MATHEMATICS | HOMOTOPY | CYCLIC BAR COMPLEX | L-INFINITY-ALGEBRAS | LIE ALGEBROIDS | GROUPOIDS

Journal Article

FORTSCHRITTE DER PHYSIK-PROGRESS OF PHYSICS, ISSN 0015-8208, 08/2019, Volume 67, Issue 8-9

A consistent description of gauge theories on coordinate dependent non-commutative (NC) space-time is a long-standing problem with a number of solutions, none...

PHYSICS, MULTIDISCIPLINARY | gauge symmetries | non-commutative geometry | L-infinity-algebras

PHYSICS, MULTIDISCIPLINARY | gauge symmetries | non-commutative geometry | L-infinity-algebras

Journal Article

ADVANCES IN THEORETICAL AND MATHEMATICAL PHYSICS, ISSN 1095-0761, 04/2017, Volume 21, Issue 2, pp. 383 - 449

Recent work applying higher gauge theory to the superstring has indicated the presence of 'higher symmetry', and the same methods work for the super-2-brane....

TRICATEGORIES | PHYSICS, MATHEMATICAL | L-INFINITY-ALGEBRAS | PHYSICS, PARTICLES & FIELDS

TRICATEGORIES | PHYSICS, MATHEMATICAL | L-INFINITY-ALGEBRAS | PHYSICS, PARTICLES & FIELDS

Journal Article

Letters in mathematical physics, ISSN 1573-0530, 2012, Volume 102, Issue 2, pp. 223 - 244

Given a strict Lie 2-algebra, we can integrate it to a strict Lie 2-group by integrating the corresponding Lie algebra crossed module. On the other hand, the...

Lie 2-groups | Theoretical, Mathematical and Computational Physics | Lie 2-algebras | Statistical Physics, Dynamical Systems and Complexity | L ∞ -algebras | Physics | Geometry | 18D10 | Secondary 18B40 | Primary 17B55 | L ∞ -morphisms | integration | Group Theory and Generalizations | crossed modules | algebras | morphisms | BRACKETS | REPRESENTATIONS | EXTENSIONS | L-infinity-morphisms | HOMOTOPY | L-infinity-algebras | PHYSICS, MATHEMATICAL

Lie 2-groups | Theoretical, Mathematical and Computational Physics | Lie 2-algebras | Statistical Physics, Dynamical Systems and Complexity | L ∞ -algebras | Physics | Geometry | 18D10 | Secondary 18B40 | Primary 17B55 | L ∞ -morphisms | integration | Group Theory and Generalizations | crossed modules | algebras | morphisms | BRACKETS | REPRESENTATIONS | EXTENSIONS | L-infinity-morphisms | HOMOTOPY | L-infinity-algebras | PHYSICS, MATHEMATICAL

Journal Article

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