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International Journal of Modern Physics A, ISSN 0217-751X, 06/2016, Volume 31, Issue 18, p. 1650105
In this paper, we realize the Lie algebra g l ( ∞ ) in one homotopy category, and we find that tau functions can be obtained from complexes in this homotopy category by taking Grothendieck group... 
fermion | tau function | boson | Lie algebra gl(∞) | Homotopy category | Lie algebra gl(infinity) | CATEGORIFICATION | PHYSICS, NUCLEAR | PHYSICS, PARTICLES & FIELDS | Algebra
Journal Article
Communications in Contemporary Mathematics, ISSN 0219-1997, 12/2014, Volume 16, Issue 6, pp. 1450007 - 1-1450007-49
...}$ may be interpreted as vector fields on P. In particular, they possess a Lie bracket and act on characteristic cohomology $\overline{H... 
characteristic cohomology | Lie-Rinehart algebras | Foliations | homotopy algebras | MATHEMATICS | LAGRANGIAN-FORMALISM | BRACKETS | MATHEMATICS, APPLIED | DEFORMATIONS | CONSERVATION-LAWS | C-SPECTRAL SEQUENCE | Algebra | Functions (mathematics) | Manifolds | Bundling | Brackets | Integrals | Mathematical analysis | Isomorphism | Fields (mathematics)
Journal Article
Algebras and representation theory, ISSN 1572-9079, 2015, Volume 19, Issue 1, pp. 1 - 5
In this paper, we construct a Lie 2-algebra associated to every Leibniz algebra via the skew-symmetrization. 
17B99 | Associative Rings and Algebras | Omni-Lie algebras | Courant algebroids | Non-associative Rings and Algebras | Commutative Rings and Algebras | Mathematics | Lie 2-algebras | Leibniz algebras | 55U15 | MATHEMATICS | HOMOTOPY | Algebra
Journal Article
Letters in Mathematical Physics, ISSN 0377-9017, 5/2017, Volume 107, Issue 5, pp. 861 - 885
Journal Article
Advances in Mathematics, ISSN 0001-8708, 08/2019, Volume 352, pp. 406 - 482
... (that is, manifolds endowed with an action of a Lie algebra g). The spaces tot(Γ(Λ•A∨)⊗RTpoly•) and tot(Γ(Λ•A∨)⊗RDpoly•) associated with a Lie pair... 
Homotopy Lie algebra | Hochschild-Kostant-Rosenberg theorem | Todd class | Kontsevich's formality theorem | Lie algebroid | Duflo's theorem | DRINFELD DOUBLES | ALGEBROIDS | INDEX THEOREM | HOMOTOPY | EHRESMANN DOUBLES | MATHEMATICS | COHOMOLOGY | DEFORMATION QUANTIZATION | ROZANSKY-WITTEN INVARIANTS | Algebra
Journal Article
2011, Mathematical surveys and monographs, ISBN 9780821805015, Volume 179, xii, 364
Book
International Journal of Geometric Methods in Modern Physics, ISSN 0219-8878, 02/2015, Volume 12, Issue 2, pp. 1550018 - 1-1550018-35
...-) Lie n-algebra homotopy theory (the true home of the "FDA"-language used in the supergravity literature... 
Lie n-algebras | Lie superalgebras | p-branes | WZW model | DIVISION-ALGEBRAS | PHYSICS, MATHEMATICAL | Tensors | Algebra | Homotopy theory | M theory | Condensates | Mathematical analysis | Mathematical models | Branes | Symmetry
Journal Article
manuscripta mathematica, ISSN 0025-2611, 5/2019, Volume 159, Issue 1, pp. 161 - 170
Let (L, d) be a differential graded Lie algebra, where $$L={\mathbb {L}}(V)$$ L = L ( V ) is free as graded Lie algebra... 
Geometry | 16W60 | Topological Groups, Lie Groups | Calculus of Variations and Optimal Control; Optimization | Mathematics, general | Algebraic Geometry | Mathematics | Number Theory | Primary 55P62 | Secondary 55P60 | MATHEMATICS | Analysis | Algebra | Mathematics - Algebraic Topology
Journal Article
Journal of Geometry and Physics, ISSN 0393-0440, 12/2012, Volume 62, Issue 12, pp. 2389 - 2400
Let g be a simplicial Lie algebra with Moore complex Ng of length k. Let G be the simplicial Lie group integrating g, such that each Gn is simply connected... 
Hypercrossed complex | Dg Lie algebra | Simplicial Lie algebra | 1-jet | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL | HOMOTOPY THEORY | GEOMETRY | Algebra
Journal Article
Geometriae Dedicata, ISSN 0046-5755, 8/2013, Volume 165, Issue 1, pp. 111 - 133
.... Equivalently, we classify 2-step nilpotent Lie algebras in dimension 7. This classification also recovers the real homotopy type of 7-dimensional 2-step nilmanifolds. 
Geometry | 11E04 | Minimal model | 17B30 | Rational homotopy | Nilmanifolds | Mathematics | Nilpotent Lie algebras | Primary: 55P62 | Secondary: 22E25 | MATHEMATICS | CLASSIFICATION | Analysis | Algebra
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
Mathematische Zeitschrift, ISSN 1432-1823, 2013, Volume 275, Issue 1-2, pp. 245 - 292
.... In this paper, we compute the rational homotopy Lie algebra of symplectomorphism groups of the 3-point blow-up of the projective plane... 
Almost complex structures | 57R17 | 57S05 | 57T20 | Homotopy type | Symplectomorphism group | Mathematics, general | Mathematics | 53D35 | TOPOLOGY | SPACE | MATHEMATICS | SYMPLECTIC BALLS | COMPLEX STRUCTURES | Analysis | Algebra
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... 
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
Forum Mathematicum, ISSN 0933-7741, 03/2017, Volume 29, Issue 2, pp. 277 - 286
...–Cartan set of a differential graded Lie algebra. We show that Euler and Miki’s identities, well-known and apparently non-related formulas, are linear combinations... 
17B01 | 55U35 | Bernoulli numbers | homotopy theory of Lie algebras | 11B68 | Gauge action | MATHEMATICS | MATHEMATICS, APPLIED | MODELS
Journal Article
DOCUMENTA MATHEMATICA, ISSN 1431-0643, 2018, Volume 23, pp. 189 - 240
In order to solve two problems in deformation theory, we establish natural structures of homotopy Lie algebras and of homotopy associative algebras on tensor products of algebras of different types... 
MATHEMATICS | infinity-morphisms | homotopy Lie algebras | Maurer-Cartan elements | Operads | homotopy associative algebras
Journal Article
Communications in Contemporary Mathematics, ISSN 0219-1997, 04/2005, Volume 7, Issue 2, pp. 145 - 165
We consider versal deformations of 0|3-dimensional L∞ algebras, also called strongly homotopy Lie algebras, which correspond precisely to ordinary (non-graded... 
algebras | Versal deformations | Strongly homotopy Lie algebras | Lie algebras | Moduli space
Journal Article
Letters in Mathematical Physics, ISSN 0377-9017, 4/2012, Volume 100, Issue 1, pp. 29 - 50
.... In particular, just as a symplectic manifold gives a Poisson algebra of functions, any 2-plectic manifold gives a Lie 2-algebra of 1-forms and functions... 
Geometry | 17B55 | 70S05 | strongly homotopy Lie algebras | Theoretical, Mathematical and Computational Physics | 53D05 | Group Theory and Generalizations | multisymplectic geometry | Statistical Physics, Dynamical Systems and Complexity | classical field theory | Physics
Journal Article
Letters in mathematical physics, ISSN 1573-0530, 2012, Volume 102, Issue 2, pp. 223 - 244
Journal Article
01/2015, ISBN 9814651443
Book
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