On some modular representations of affine Kac-Moody algebras at the critical level
On spherical nilpotent orbits and beyond
We continue investigations that are concerned with the complexity of nilpotent orbits in semisimple Lie algebras. We give a characterization of the spherical nilpotent orbits in terms of minimal Levi subalgebras intersecting them. This provides a kind of canonical form for such orbits. A description minimal non-spherical orbits in all simple Lie algebras is obtained. The theory developed for the adjoint representation is then extended to Vinberg’s -groups. This yields a description of spherical...
On subsemigroups of semisimple Lie groups
On tangent cones to Schubert varieties in type
We consider tangent cones to Schubert subvarieties of the flag variety , where is a Borel subgroup of a reductive complex algebraic group of type , or . We prove that if and form a good pair of involutions in the Weyl group of then the tangent cones and to the corresponding Schubert subvarieties of do not coincide as subschemes of the tangent space to at the neutral point.
On tensor representations of knot algebras.
On the adjoint map of homotopy abelian DG-Lie algebras
We prove that a differential graded Lie algebra is homotopy abelian if its adjoint map into its cochain complex of derivations is trivial in cohomology. The converse is true for cofibrant algebras and false in general.
On the annihilators of the simple subquotients of the principal series
On the asymptotics of the number of p̅-core partitions of integers
On the basic algebraic operations in solvable Lie groups.
On the basic representation of the affine Kac-Moody Lie algebras
On the Bernstein-Gelfand-Gelfand resolution and the Duflo sum formula
On the braiding on a Hopf algebra in a braided category.
On the Cartan subalgebras of Lie algebras over small fields.
On the center of . (Sur le centre de .)
On the centralizer of K in the universal enveloping algebra of SO(n,1) and SU(n,1).
On the characteristic polynomials of orbital varieties
On the Characterization of Primitive Ideals in Enveloping Algebras.
On the Chevalley restriction theorem.
On the classification of -dimensional -manifold algebras
-manifold algebras are focused on the algebraic properties of the tangent sheaf of -manifolds. The local classification of 3-dimensional -manifolds has been given in A. Basalaev, C. Hertling (2021). We study the classification of 3-dimensional -manifold algebras over the complex field .
On the classification of 3-dimensional coloured Lie algebras
In this paper, complex 3-dimensional Γ-graded ε-skew-symmetric and complex 3-dimensional Γ-graded ε-Lie algebras with either 1-dimensional or zero homogeneous components are classified up to isomorphism.