On solutions of the KZ and qKZ equations at level zero
On solutions to the twisted Yang-Baxter equation
On solvability of Lie rings with an automorphism of finite order.
On Solvable Generalized Calabi-Yau Manifolds
We give an example of a compact 6-dimensional non-Kähler symplectic manifold that satisfies the Hard Lefschetz Condition. Moreover, it is showed that is a special generalized Calabi-Yau manifold.
On some anticyclic operads.
On some causal and conformal groups.
On some classes of nilpotent Leibniz algebras.
On some formulas in the Hall algebra of the Kronecker algebra.
On Some Generalizations of Lie Algebras
On some modular representations of affine Kac-Moody algebras at the critical level
On some properties of the upper central series in Leibniz algebras
This article discusses the Leibniz algebras whose upper hypercenter has finite codimension. It is proved that such an algebra includes a finite dimensional ideal such that the factor-algebra is hypercentral. This result is an extension to the Leibniz algebra of the corresponding result obtained earlier for Lie algebras. It is also analogous to the corresponding results obtained for groups and modules.
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 Andrunakievich lemma for linear Jordan rings.
On the annihilators of the simple subquotients of the principal series
On the associative Nijenhuis relation.
On the asymptotics of the number of p̅-core partitions of integers