We explore the (noncommutative) geometry of locally simple representations of the diagonal
locally finite Lie algebras,, and. Let be one of these Lie algebras, and let be the non-zero …

We introduce a new type of noncommutative Poisson structure on associative algebras. It
induces Poisson structures on the moduli spaces classifying semisimple modules. Path …

We initiate a unified, axiomatic study of noncommutative algebras R whose prime spectra
are, in a natural way, finite unions of commutative noetherian spectra. Our results illustrate …

We prove most of Lusztig's conjectures on the canonical basis in homology of a Springer
fiber. The conjectures predict that this basis controls numerics of representations of the Lie …

In [math. AG/0010030; Math. Z., to appear] R. Bocklandt and the author proved that certain
quotient varieties of representations of deformed preprojective algebras are coadjoint orbits …

Given a noncommutative Hamiltonian space $ A $, we show that the conjecture``{\it
quantization commutes with reduction}''holds on $ A $. We also construct a semi-product …

This article sets out to understand the categories $\QGr A $ where $ A $ is either a monomial
algebra or a path algebra of finite Gelfand-Kirillov dimension. The principle questions are: 1) …

The aim of this paper is to introduce and study Lie algebras over noncommutative rings. For
any Lie algebra g sitting inside an associative algebra A and any associative algebra F we …

The aim of this paper is to introduce and study Lie algebras and Lie groups over
noncommutative rings. For any Lie algebra g sitting inside an associative algebra A and any …

We consider some special type extensions of an arbitrary Lie algebra, which we call
universal extensions. We show that these extensions are in one-to-one correspondence with …