On Lie powers of regular modules in characteristic 2
On Linear and Quadratic Jordan Division Algebras.
On matrix Lie rings over a commutative ring that contain the special linear Lie ring
Let be an associative and commutative ring with , a subring of such that , an integer. The paper describes subrings of the general linear Lie ring that contain the Lie ring of all traceless matrices over .
On maximal subalgebras of central simple Malcev algebras.
In this paper the structure of the maximal elements of the lattice of subalgebras of central simple non-Lie Malcev algebras is considered. Such maximal subalgebras are studied in two ways: first by using theoretical results concerning Malcev algebras, and second by using the close connection between these simple non-Lie Malcev algebras and the Cayley-Dickson algebras, which have been extensively studied (see [4]).
On multiplicities of simple subquotients in generalized Verma modules
We reduce the problem on multiplicities of simple subquotients in an -stratified generalized Verma module to the analogous problem for classical Verma modules.
On Nambu bracket representations of 3-algebras.
On nilpotent filiform Lie algebras of dimension eight.
On normal abelian subgroups in parabolic groups
Let be a reductive algebraic group, a parabolic subgroup of with unipotent radical , and a closed connected subgroup of which is normalized by . We show that acts on with finitely many orbits provided is abelian. This generalizes a well-known finiteness result, namely the case when is central in . We also obtain an analogous result for the adjoint action of on invariant linear subspaces of the Lie algebra of which are abelian Lie algebras. Finally, we discuss a connection...
On Ol'shanskii's semigroup.
On one-sided division infinite-dimensional normed real algebras.
In this note we introduce the concept of Cayley homomorphism which is closely related with those of composition algebra and normalized orthogonal multiplication. The key result shows the existence of certain types of Cayley homomorphisms for infinite dimension. As an application we prove the existence of left division infinite-dimensional complete normed real algebras with left unity.
On porcupine varieties in Lie algebras.
On positive and critical theories of some classes of rings.
On Prealgebraic Groups.
On prime -graded Lie algebras of growth one.
On quantum and classical Poisson algebras
Results on derivations and automorphisms of some quantum and classical Poisson algebras, as well as characterizations of manifolds by the Lie structure of such algebras, are revisited and extended. We prove in particular a somewhat unexpected fact that the algebras of linear differential operators acting on smooth sections of two real vector bundles of rank 1 are isomorphic as Lie algebras if and only if the base manifolds are diffeomorphic, whether or not the line bundles themselves are isomorphic....
On quantum weyl algebras and generalized quons
The model of generalized quons is described in an algebraic way as certain quasiparticle states with statistics determined by a commutation factor on an abelian group. Quantization is described in terms of quantum Weyl algebras. The corresponding commutation relations and scalar product are also given.
On quasi-analytic vectors for some classes of operators
On rational solutions of Yang-Baxter equation for sl(n).
On real Cartan factors.
On Real Forms of JB*-triples.