On affine Kac-Moody Lie algebras
On Algebraic Power-Associative and Jordan Algebras with Semi-Normal Functionals.
On Algebras all of Whose Subalgebras are Simple; Some Solutions of Plonka's Problem
On annihilators in Jordan algebras.
In this paper we prove that a nondegenerate Jordan algebra satisfying the descending chain condition on the principal inner ideals, also satisfies the ascending chain condition on the annihilators of the principal inner ideals. We also study annihilators in Jordan algebras without nilpotent elements and in JB-algebras.
On automorphism groups of non-associative Boolean rings.
On automorphisms of Weyl algebra
On basic and axiomatic ranks of nilpotent varieties of Lie algebras
On bilinear biquandles
We define a type of biquandle which is a generalization of symplectic quandles. We use the extra structure of these bilinear biquandles to define new knot and link invariants and give some examples.
On bounded generalized Harish-Chandra modules
Let be a complex reductive Lie algebra and be any reductive in subalgebra. We call a -module bounded if the -multiplicities of are uniformly bounded. In this paper we initiate a general study of simple bounded -modules. We prove a strong necessary condition for a subalgebra to be bounded (Corollary 4.6), i.e. to admit an infinite-dimensional simple bounded -module, and then establish a sufficient condition for a subalgebra to be bounded (Theorem 5.1). As a result we are able to...
On brane solutions related to non-singular Kac-Moody algebras.
On category for cyclotomic rational Cherednik algebras
We study equivalences for category of the rational Cherednik algebras of type : a highest weight equivalence between and for and an action of on an explicit non-empty Zariski open set of parameters ; a derived equivalence between and whenever and have integral difference; a highest weight equivalence between and a parabolic category for the general linear group, under a non-rationality assumption on the parameter . As a consequence, we confirm special cases of conjectures...
On centerless commutative automorphic loops
In this short paper, we survey the results on commutative automorphic loops and give a new construction method. Using this method, we present new classes of commutative automorphic loops of exponent with trivial center.
On certain class of unitarizable representations of the Lie algebra
On characteristic identities for Lie algebras
On characterization of Poisson and Jacobi structures
We characterize Poisson and Jacobi structures by means of complete lifts of the corresponding tensors: the lifts have to be related to canonical structures by morphisms of corresponding vector bundles. Similar results hold for generalized Poisson and Jacobi structures (canonical structures) associated with Lie algebroids and Jacobi algebroids.
On Cherednik-Macdonald-Mehta identities.
On classical -matrices with parabolic carrier.
On classification of metabelian Lie algebras.
On closedness and simple connectedness of adjoint and coadjoint orbits.
On commutation relations for 3-graded Lie algebras.