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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
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
Journal Article
Letters in Mathematical Physics, ISSN 0377-9017, 5/2017, Volume 107, Issue 5, pp. 861 - 885
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
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
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
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
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
Journal Article
by Bi, YH and Sheng, YH
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
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
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
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
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
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
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
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
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
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
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
Journal Article
Letters in mathematical physics, ISSN 1573-0530, 2012, Volume 102, Issue 2, pp. 223 - 244
Journal Article
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