arXiv subjects

Sergiy Ovsienko

Publications and source records attributed to Sergiy Ovsienko.

3 recordsLinked to original sources

arXiv2016

Noncommutative Noether's problem for complex reflection groups

We solve the noncommutative Noether's problem for the reflection groups by showing that the skew field of the invariants of the Weyl algebra under the action of any reection group is a Weyl field, that is isomorphic to a skew field of some Weyl algebra over a transcendental extension of the ground field. We also extend this result to the invariants of the ring of differential operators on any dimensional torus.The results are applied to obtain analogs of the Gelfand-Kirillov Conjecture for Cherednik algebras and Galois algebras.

math.RA↗

arXiv2014

Quasi-hereditary algebras, exact Borel subalgebras, A-infinity-categories and boxes

Highest weight categories arising in Lie theory are known to be associated with finite dimensional quasi-hereditary algebras such as Schur algebras or blocks of category $\mathcal O$. An analogue of the PBW theorem will be shown to hold for quasi-hereditary algebras: Up to Morita equivalence each such algebra has an exact Borel subalgebra. The category $\mathcal{F}(Δ)$ of modules with standard (Verma, Weyl, \dots) filtration, which is exact, but rarely abelian, will be shown to be equivalent to the category of representations of a directed box. This box is constructed as a quotient of a dg algebra associated with the $A_{\infty}$-structure on $\mathcal{F}(Δ)$. Its underlying algebra is an exact Borel subalgebra.

math.RT↗

arXiv2008

A construction of quotient A_infinity-categories

We construct an A_infinity-category D(C|B) from a given A_infinity-category C and its full subcategory B. The construction is similar to a particular case of Drinfeld's quotient of differential graded categories. We use D(C|B) to construct an A_infinity-functor of K-injective resolutions of a complex. The conventional derived category is obtained as the 0-th cohomology of the quotient of differential graded category of complexes over acyclic complexes.

math.CT↗