119 citations · 298 across the 33 of their papers we have counts for
35 papers
Dual reflection groups for three-dimensional Artin--Schelter regular algebras
Lucas Buzaglo, Daniel Rogalski
By definition, a dual reflection group is a finite group which grades an Artin--Schelter regular algebra such that the identity component is again regular. In this paper,…
Coactions of cocommutative Hopf algebras on skew polynomial rings
Lucas Buzaglo, Daniel Rogalski
We classify the cocommutative Hopf algebras which coact inner-faithfully on (one-parameter) skew polynomial rings $A_q(n) = \Bbbk \langle x_1,\dots,x_n \rangle/(x_j x_i - q x_i x_j…
Homological Integrals for Weak Hopf Algebras
Daniel Rogalski, Robert Won, James J. Zhang
We introduce the notion of a homological integral for an infinite-dimensional weak Hopf algebra and use the homological integral to prove several structure theorems. For example, w…
Closed subcategories of quotient categories
Daniel Rogalski
We study the spectrum of closed subcategories in a quasi-scheme, i.e. a Grothendieck category . The closed subcategories are the direct analogs of closed subschemes in the commu…
The domain and prime properties for Koszul rings and algebras
Manuel L. Reyes, Daniel Rogalski
We establish a technique to prove that a Koszul graded ring is prime or a domain using information about its Koszul dual. This is based on a general categorical result that expands…
Artin-Schelter Regular Algebras
Daniel Rogalski
Artin-Schelter regular algebras can be thought of as noncommutative versions of commutative polynomial rings, modeled after the special homological properties polynomial rings have…