On the Mulitplicity of Zeros of Polynomials over Arbitrary Finite Dimensional K-Algebras.
On the multiplicative structure of finite division rings.
On the multiplier of a Lie algebra.
On the nilpotency of certain subalgebras of Kac-Moody Lie algebras.
On the nilpotent residuals of all subalgebras of Lie algebras
Let denote the class of nilpotent Lie algebras. For any finite-dimensional Lie algebra over an arbitrary field , there exists a smallest ideal of such that . This uniquely determined ideal of is called the nilpotent residual of and is denoted by . In this paper, we define the subalgebra . Set . Define for . By denote the terminal term of the ascending series. It is proved that if and only if is nilpotent. In addition, we investigate the basic properties of a Lie algebra...
On the principal bundles over a flag manifold.
On the principle of stability of invariance of physical systems
On the problem of classifying simple compact quantum groups
We review the notion of simple compact quantum groups and examples, and discuss the problem of construction and classification of simple compact quantum groups.
On the q-exponential of matrix q-Lie algebras
In this paper, we define several new concepts in the borderline between linear algebra, Lie groups and q-calculus.We first introduce the ring epimorphism r, the set of all inversions of the basis q, and then the important q-determinant and corresponding q-scalar products from an earlier paper. Then we discuss matrix q-Lie algebras with a modified q-addition, and compute the matrix q-exponential to form the corresponding n × n matrix, a so-called q-Lie group, or manifold, usually with q-determinant...
On the radical of J*-triples.
On the rational homotopy Lie algebra of spaces with finite dimensional rational cohomology and homotopy
The problem of the characterization of graded Lie algebras which admit a realization as the homotopy Lie algebra of a space of type is discussed. The central results are formulated in terms of varieties of structure constants, several criterions for concrete algebras are also deduced.
On the regularity and rationality of certain elements of finite order in Lie groups.
On the Riemann-Lie algebras and Riemann-Poisson Lie groups.
On the rings on torsion-free groups
On the Scole of a Noncommutative Jordan Algebra.
On the set-theoretical Yang-Baxter equation.
On the socle of a Jordan pair.
On the Specht property of varieties of commutative alternative algebras over a field of characteristic 3 and commutative Moufang loops.
On the spectral set of a solvable Lie algebra of operators.
On the stability of subgroup actions on certain quasihomogeneous -varieties.