A skew Calabi–Yau algebra is a generalization of a Calabi–Yau algebra which allows for a
non-trivial Nakayama automorphism. We prove three homological identities about the …

This paper concerns conditions on the action of a finite dimensional semisimple Hopf
algebra on an Artin–Schelter regular algebra that force the subring of invariants to satisfy the …

Nakayama automorphism and applications Page 1 TRANSACTIONS OF THE AMERICAN
MATHEMATICAL SOCIETY Volume 369, Number 4, April 2017, Pages 2425–2460 http://dx.doi.org/10.1090/tran/6718 …

We introduce the reflexive hull discriminant as a tool to study noncommutative algebras that
are finitely generated, but not necessarily free, over their centers. As an example, we …

We prove that the algebra of integro-differential operators on a polynomial algebra is a
prime, central, catenary, self-dual, non-Noetherian algebra of classical Krull dimension n …

In the 1960s Maurice Auslander proved the following important result. Let $ R $ be the
commutative polynomial ring $\mathbb {C}[x_1,\dots, x_n] $, and let $ G $ be a finite small …

When $ A=\Bbbk [x_1,\ldots, x_n] $ and $ G $ is a small subgroup of $\operatorname {GL} _n
(\Bbbk) $, Auslander's Theorem says that the skew group algebra $ A\# G $ is isomorphic to …

This is survey of results that extend notions of the classical invariant theory of linear actions
by finite groups on k [x1,..., xn] to the setting of finite group or Hopf algebra H actions on an …

It is known that every 3-dimensional noetherian Calabi–Yau algebra generated in degree 1
is isomorphic to a Jacobian algebra of a superpotential. Recently, SP Smith and the first …

We introduce the ozone group of a noncommutative algebra, defined as the group of
automorphisms of, which fix every element of its center. In order to initiate the study of ozone …