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 representation theory of quantum groups at roots of unity
Irreducible representations of quantum groups (in Woronowicz’ approach) were classified in J.Wang, B.Parshall, Memoirs AMS 439 in the case of q being an odd root of unity. Here we find the irreducible representations for all roots of unity (also of an even degree), as well as describe “the diagonal part” of the tensor product of any two irreducible representations. An example of a not completely reducible representation is given. Non-existence of Haar functional is proved. The corresponding representations...
On representations of Lie algebras of a generalized Tavis-Cummings model.
On representations of restricted Lie superalgebras
Simple modules for restricted Lie superalgebras are studied. The indecomposability of baby Kac modules and baby Verma modules is proved in some situation. In particular, for the classical Lie superalgebra of type , the baby Verma modules are proved to be simple for any regular nilpotent -character and typical weight . Moreover, we obtain the dimension formulas for projective covers of simple modules with -characters of standard Levi form.
On -representations of the Hopf -algebra associated with the quantum group
On *-representations of : more real forms
The main goal of this paper is to do the representation-theoretic groundwork for two new candidates for locally compact (nondiscrete) quantum groups. These objects are real forms of the quantized universal enveloping algebra and do not have real Lie algebras as classical limits. Surprisingly, their representations are naturally described using only bounded (in one case only two-dimensional) operators. That removes the problem of describing their Hopf structure ’on the Hilbert space level’([W])....
On Root Systems.
On roots of the automorphism group of a circular domain in
We study the properties of the group Aut(D) of all biholomorphic transformations of a bounded circular domain D in containing the origin. We characterize the set of all possible roots for the Lie algebra of Aut(D). There exists an n-element set P such that any root is of the form α or -α or α-β for suitable α,β ∈ P.
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 classes of nilpotent Leibniz algebras.
On some formulas in the Hall algebra of the Kronecker algebra.
On Some Generalizations of Lie Algebras