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8 papers · 1 filter
On formal codegrees of fusion categories
Victor Ostrik
We prove a general result which implies that the global and Frobenius-Perron dimensions of a fusion category generate Galois invariant ideals in the ring of algebraic integers.
Weakly group-theoretical and solvable fusion categories
Pavel Etingof, Dmitri Nikshych, Victor Ostrik
We introduce two new classes of fusion categories which are obtained by a certain procedure from finite groups - weakly group-theoretical categories and solvable categories. These…
Noncommutative Dunkl operators and braided Cherednik algebras
Yuri Bazlov, Arkady Berenstein
We introduce braided Dunkl operators that are acting on a q-polynomial algebra and q-commute. Generalizing the approach of Etingof and Ginzburg, we explain the q-commutation phenom…
Lie algebras and Lie groups over noncommutative rings
Arkady Berenstein, Vladimir Retakh
The aim of this paper is to introduce and study Lie algebras and Lie groups over noncommutative rings. For any Lie algebra sitting inside an associative algebra and any a…
Dual canonical bases and Kazhdan-Lusztig polynomials
Jonathan Brundan
We derive a formula for the entries of the (unitriangular) transition matrices between the standard monomial and dual canonical bases of the irreducible polynomial representations…
Quasicoherent sheaves on complex noncommutative two-tori
Alexander Polishchuk
We introduce the notion of a quasicoherent sheaf on a complex noncommutative two-torus as an ind-object in the category of holomorphic vector bundles on . Extending the resu…