60 citations · 582 across the 131 of their papers we have counts for
7 papers · 1 filter
Some homological properties of category O. IV
Kevin Coulembier, Volodymyr Mazorchuk
We study projective dimension and graded length of structural modules in parabolic-singular blocks of the BGG category O. Some of these are calculated explicitly, others are expres…
Dualities and derived equivalences for category O
Kevin Coulembier, Volodymyr Mazorchuk
We determine the Ringel duals for all blocks in the parabolic versions of the BGG category O associated to a reductive finite dimensional Lie algebra. In particular we find that, c…
Parabolic projective functors in type A
Tobias Kildetoft, Volodymyr Mazorchuk
We classify projective functors on the regular block of Rocha-Caridi's parabolic version of the BGG category in type . In fact, we show that, in type , the rest…
Koszul duality for semidirect products and generalized Takiff algebras
Jacob Greenstein, Volodymyr Mazorchuk
We obtain Koszul-type dualities for categories of graded modules over a graded associative algebra which can be realized as the semidirect product of a bialgebra coinciding with it…
Graded simple Lie algebras and graded simple representations
Volodymyr Mazorchuk, Kaiming Zhao
For any finitely generated abelian group , we reduce the problem of classification of -graded simple Lie algebras over an algebraically closed field of "good" characteristic…
On the number of principal ideals in d-tonal partition monoids
Chwas Ahmed, Paul Martin, Volodymyr Mazorchuk
For a positive integer , a non-negative integer and a non-negative integer , we study the number of principal ideals; and the number o…