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