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 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 set-theoretical Yang-Baxter equation.
On the spectral set of a solvable Lie algebra of operators.
On the stability of subgroup actions on certain quasihomogeneous -varieties.
On the structure of an ...-stratified generalized Verma module over Lie algebra sl(n, C).
On the structure of graded transitive Lie algebras.
On the Structure of Reduced ...-Ternary Algebras of Degree > 2.
On the structure of solvable Lie algebras.
On the structure of transitively differential algebras.
On the uniqueness of the -dimensional supertorus associated to a nontrivial representation of its underlying 2-torus, and having nontrivial odd brackets.
On the unitarizability of derived functor modules.
On the vanishing of extensions of modules over reduced enveloping algebras.
On the variety of 3-dimensional Lie algebras.
On the variety of lagrangian subalgebras, I
On the variety of lagrangian subalgebras, II
On two possible constructions of the quantum semigroup of all quantum permutations of an infinite countable set
Two different models for a Hopf-von Neumann algebra of bounded functions on the quantum semigroup of all (quantum) permutations of infinitely many elements are proposed, one based on projective limits of enveloping von Neumann algebras related to finite quantum permutation groups, and the second on a universal property with respect to infinite magic unitaries.