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- 17-XX Nonassociative rings and algebras
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L’objet de cet article est de calculer la cohomologie et la K-théorie équivariantes des variétés de Bott-Samelson (théorèmes 3.3 et 4.3) et d’en déduire des résultats sur les variétés de drapeaux des groupes de Kac-Moody. Dans la section 3, on retrouve la formule de restriction aux points fixes de la base de (théorème 3.9) prouvée par Sara Billey dans [4]. Dans la section 4, on donne l’expression explicite de la restriction aux points fixes de la base de définie par Kostant et Kumar dans...
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.
We compute the unique nonzero cohomology group of a generic - linearized locally free -module, where is the identity component of a complex classical Lie supergroup and is an arbitrary parabolic subsupergroup. In particular we prove that for this cohomology group is an irreducible -module. As an application we generalize the character formula of typical irreducible -modules to a natural class of atypical modules arising in this way.
Hom-Lie algebra (superalgebra) structure appeared naturally in -deformations, based on -derivations of Witt and Virasoro algebras (superalgebras). They are a twisted version of Lie algebras (superalgebras), obtained by deforming the Jacobi identity by a homomorphism. In this paper, we discuss the concept of -derivation, a representation theory, and provide a cohomology complex of Hom-Lie superalgebras. Moreover, we study central extensions. As application, we compute derivations and the second...
We consider the Lie algebra of inner derivations of the -fold tensor product of Manin quantum planes and compute its second cohomology group with trivial coefficients.
Natural graded Lie brackets on the space of cochains of n-Leibniz and n-Lie algebras are introduced. It turns out that these brackets agree under the natural embedding introduced by Gautheron. Moreover, n-Leibniz and n-Lie algebras turn to be canonical structures for these brackets in a similar way in which associative algebras (respectively, Lie algebras) are canonical structures for the Gerstenhaber bracket (respectively, Nijenhuis-Richardson bracket).
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