Quantization of cohomology in semi-simple Lie algebras.
Milson, R., Richter, D. (1998)
Journal of Lie Theory
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Milson, R., Richter, D. (1998)
Journal of Lie Theory
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Simon Covez (2013)
Annales de l’institut Fourier
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This article gives a local answer to the coquecigrue problem for Leibniz algebras, that is, the problem of finding a generalization of the (Lie) group structure such that Leibniz algebras are the corresponding tangent algebra structure. Using links between Leibniz algebra cohomology and Lie rack cohomology, we generalize the integration of a Lie algebra into a Lie group by proving that every Leibniz algebra is isomorphic to the tangent Leibniz algebra of a local Lie rack. This article...
Benayed, Miloud (1997)
Journal of Lie Theory
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Malakhaltsev, M.A. (1999)
Lobachevskii Journal of Mathematics
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Junxia Zhu, Liangyun Chen (2021)
Czechoslovak Mathematical Journal
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We study Hom-Lie superalgebras of Heisenberg type. For 3-dimensional Heisenberg Hom-Lie superalgebras we describe their Hom-Lie super structures, compute the cohomology spaces and characterize their infinitesimal deformations.
Carlo Alberto Cremonini (2022)
Archivum Mathematicum
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This note is based on a short talk presented at the “42nd Winter School Geometry and Physics” held in Srni, Czech Republic, January 15th–22nd 2022. We review the notion of Lie superalgebra cohomology and extend it to different form complexes, typical of the superalgebraic setting. In particular, we introduce pseudoforms as infinite-dimensional modules related to sub-superalgebras. We then show how to extend the Koszul-Hochschild-Serre spectral sequence for pseudoforms as a computational...
José Adolfo de Azcárraga, José Manuel Izquierdo, Juan Carlos Pérez Bueno (2001)
RACSAM
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En esta nota se presenta en primer lugar una introducción autocontenida a la cohomología de álgebras de Lie, y en segundo lugar algunas de sus aplicaciones recientes en matemáticas y física.
Kim, Yunhyong (2004)
Journal of Lie Theory
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Jerry M. Lodder (1998)
Annales de l'institut Fourier
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We propose a definition of Leibniz cohomology, , for differentiable manifolds. Then becomes a non-commutative version of Gelfand-Fuks cohomology. The calculations of reduce to those of formal vector fields, and can be identified with certain invariants of foliations.
Marius Crainic, Ieke Moerdijk (2008)
Journal of the European Mathematical Society
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We introduce a new cohomology for Lie algebroids, and prove that it provides a differential graded Lie algebra which “controls” deformations of the structure bracket of the algebroid.