Cohomology Groups of Infinite Dimensional Algebras.
Cohomology groups of reduced enveloping algebras.
Cohomology of Bimodules Over Enveloping Algebras.
Cohomology of for classical complex Lie supergroups and characters of some atypical -modules
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.
Cohomology of Hom-Lie superalgebras and -deformed Witt superalgebra
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...
Cohomology of infinitesimal algebraic groups.
Cohomology of some nilpotent Lie algebras.
Cohomology of tensor product of quantum planes
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.
Cohomology of the Lie Algebra of Vector Fields on a Complex Manifold.
Cohomology ring of n-Lie algebras.
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).
Colored partitions and a generalization of the braid arrangement.
Coloured generalised Young diagrams for affine Weyl-Coxeter groups.
Combinatorial bases of modules for affine Lie algebra B 2(1)
We construct bases of standard (i.e. integrable highest weight) modules L(Λ) for affine Lie algebra of type B 2(1) consisting of semi-infinite monomials. The main technical ingredient is a construction of monomial bases for Feigin-Stoyanovsky type subspaces W(Λ) of L(Λ) by using simple currents and intertwining operators in vertex operator algebra theory. By coincidence W(kΛ0) for B 2(1) and the integrable highest weight module L(kΛ0) for A 1(1) have the same parametrization of combinatorial bases...
Combinatorial constructions of weight bases: the Gelfand-Tsetlin basis.
Combinatorial interpretations for rank-two cluster algebras of affine type.
Combinatorics, superalgebras, invariant theory and representation theory.
Commentary to: Generalized derivations of Lie triple systems
Comments on the Links Between Modular Invariants, Simple Factors in the Jacobian of Fermat Curves, and Rational Triangular Billiards
Commutator algebras arising from splicing operations
We prove that the variety of Lie algebras arising from splicing operation coincides with the variety CM of centreby-metabelian Lie algebras. Using these Lie algebras we find the minimal dimension algebras generated the variety CM and the variety of its associative envelope algebras. We study the splicing n-ary operation. We show that all n-ary (n > 2) commutator algebras arising from this operation are nilpotent of index 3. We investigate the generalization of the splicing n-ary operation, and...
Commutator representations of covariant differential calculi