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Proceedings of the London Mathematical Society, ISSN 0024-6115, 04/2011, Volume 102, Issue 4, pp. 697 - 730
In this paper we study the homological properties of various natural modules associated to the Fourier algebra of a locally compact group... 
MATHEMATICS | UNITARY REPRESENTATIONS | SPACES | AMENABILITY | LOCALLY COMPACT-GROUPS | L-INFINITY G | SUBSPACES
Journal Article
Studia Mathematica, ISSN 0039-3223, 2010, Volume 199, Issue 3, pp. 241 - 265
...) algebras for pointwise multiplication. We characterize in terms of the matrix V = (v(n))(n) when an algebra k(p)(V) is unital, locally m-convex, a Q-algebra, has a continuous... 
Automatic continuity | Characters | LB-spaces | Riesz algebras | Regular ideals | Coechelon spaces | modules | Maximal ideals | Q-algebras | Topological algebras | l(infinity)-modules | INDUCTIVE LIMITS | coechelon spaces | regular ideals | ORTHOGONAL BASES | SCHAUDER BASES | MATHEMATICS | characters | topological algebras | maximal ideals | automatic continuity
Journal Article
Journal of Homotopy and Related Structures, ISSN 2193-8407, 10/2014, Volume 9, Issue 2, pp. 285 - 298
An $$L_{\infty }$$ module is a natural generalization of a Lie module. It is a language equivalent to the representation theory of $$L_{\infty }$$ algebras... 
Algebra | Functional Analysis | Algebraic Topology | 17B10 | Mathematics | Representation | Number Theory | 55P43 | Module | Homomorphism | 18G55 | L-infinity
Journal Article
Letters in Mathematical Physics, ISSN 0377-9017, 11/2012, Volume 102, Issue 2, pp. 223 - 244
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 algebra together with a module... 
Links | Milnor fibers | Weight filtration | Deformation theory | Fundamental group | L-infinity algebras and modules | TOPOLOGY | MATHEMATICS | SYSTEMS | HOMOTOPY | COHOMOLOGY JUMP LOCI
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... 
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, 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... 
[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
Functional Analysis and Its Applications, ISSN 0016-2663, 4/2019, Volume 53, Issue 2, pp. 102 - 109
.... The main result is as follows: a Banach module over a relatively amenable Banach algebra which is topologically flat as a Banach space is topologically flat as a Banach module... 
Banach module | Functional Analysis | ℒ ∞ g -space | Analysis | Mathematics | amenability | ℒ 1 g -space | topological flatness | MATHEMATICS | MATHEMATICS, APPLIED | OPERATORS | L-1(g)-space | L-infinity(g)-space | Algebra
Journal Article
Compositio mathematica, ISSN 0010-437X, 02/2013, Volume 149, Issue 2, pp. 264 - 294
.... To do so, we develop a theory of butterflies for 2-term L∞-algebras. In particular, we obtain a new description of the bicategory of 2-term L∞-algebras... 
Lie 2-group | L ∞-algebra | Lie crossed module | connected cover | Lie butterfly | Lie 2-algebra | MATHEMATICS | L-infinity-algebra | Algebraic group theory | Construction | Butterflies | Lie groups
Journal Article
JOURNAL OF HOMOTOPY AND RELATED STRUCTURES, ISSN 2193-8407, 2014, Volume 9, Issue 2, pp. 285 - 298
An module is a natural generalization of a Lie module. It is a language equivalent to the representation theory of algebras... 
LIE-ALGEBRAS | MATHEMATICS | Representation | Module | Homomorphism | L-infinity
Journal Article
Communications in Algebra, ISSN 0092-7872, 10/2014, Volume 42, Issue 10, pp. 4333 - 4349
We consider the class of ℤ p -modules with partial decomposition bases. This class was developed in order to extend Barwise and Eklof's classification of torsion groups in L ∞ω... 
Warfield modules | Primary 03C52 | Secondary 20K21 | Partial decomposition basis | Partial isomorphism | Moore modules | k-modules | MATHEMATICS | ABELIAN-GROUPS | L-INFINITY-OMEGA(DELTA) | Decomposition | Algebra | Torsion | Modules | Classification
Journal Article
Differential Geometry and its Applications, ISSN 0926-2245, 10/2016, Volume 48, pp. 72 - 86
.... When the line bundle is trivial we shall speak of higher Jacobi brackets. These brackets are understood furnishing the module of sections with an L... 
[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
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
Journal of Geometry and Physics, ISSN 0393-0440, 02/2013, Volume 64, Issue 1, pp. 155 - 173
... −1 and 0 on degree 1 NQ-manifolds. In a more conventional language this means: strict actions of Lie algebra crossed modules on Lie algebroids... 
Double Lie algebroid | Higher Lie group action | NQ-manifold | Higher Lie algebra action | Lie algebroid | BRACKETS | MATHEMATICS, APPLIED | GROUPOIDS | PHYSICS, MATHEMATICAL | L-INFINITY-ALGEBRAS | Algebra
Journal Article
ALGEBRA COLLOQUIUM, ISSN 1005-3867, 06/2019, Volume 26, Issue 2, pp. 195 - 230
...)] of any A-module E induces a Lie algebra module structure on H-CE(center dot)(A, E). Moreover, Atiyah classes are invariant under gauge equivalent A-compatible... 
MATHEMATICS | MATHEMATICS, APPLIED | homotopical algebra | REPRESENTATIONS | PBW | L-infinity-algebra | Atiyah class
Journal Article
数学学报:英文版, ISSN 1439-8516, 2012, Volume 28, Issue 3, pp. 477 - 486
Journal Article
Communications in Algebra, ISSN 0092-7872, 08/2016, Volume 44, Issue 8, pp. 3262 - 3277
... X such that ⟨ X ⟩ is locally nice in G and G/ ⟨ X ⟩ is simply presented. If the groups are ℤp-modules (where ℤp is the ring of integers localized at the prime p... 
k-Subgroup | Secondary: 20K21 | Decomposition set | Partial decomposition basis | Primary: 03C52 | Partial isomorphism | Warfield group | Moore group | Partial subbasis | k-Group | MATHEMATICS | MODULES | ABELIAN-GROUPS | L-INFINITY-OMEGA(DELTA) | Uniqueness theorems | Decomposition | Algebra | Torsion | Subgroups | Classification
Journal Article
Compositio mathematica, ISSN 0010-437X, 05/2012, Volume 148, Issue 3, pp. 807 - 834
.... We show that every connected and étale stacky Lie group is equivalent to a crossed module of the form (Γ,G) where Γ... 
Lie 2-group | categorified group | stacky Lie group | crossed modules | strictification | MATHEMATICS | BRACKETS | INTEGRABILITY | 2-GROUPS | L-INFINITY-ALGEBRAS | Mathematics | Stacks | Equivalence | Modules | Lie groups
Journal Article
Advances in Mathematics, ISSN 0001-8708, 06/2019, Volume 349, pp. 869 - 910
... using mixed Hodge diagrams and methods of L∞ algebras. We apply it in two geometric situations... 
Hodge theory | [formula omitted] algebras | Representation varieties | Complex algebraic geometry | Formal deformation theory | Fundamental groups | MATHEMATICS | L-infinity algebras | Algebraic Geometry | Mathematics
Journal Article
by Lada, T
APPLIED CATEGORICAL STRUCTURES, ISSN 0927-2852, 02/2004, Volume 12, Issue 1, pp. 29 - 34
It is shown that the direct sum of an L-infinity algebra and a module over it has a natural L-infinity algebra structure. 
LIE-ALGEBRAS | MATHEMATICS, APPLIED | L-infinity module | L-infinity algebra
Journal Article
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