The Nakayama automorphism of a class of graded algebras

Abstract

The Nakayama automorphism of a class of connected graded Artin-Schelter regular algebras is calculated explicitly.

Nakayama automorphisms of graded Ore extensions of Koszul Artin-Schelter regular algebras

“…However, the computation of Nakayama automorphisms is always hard. There is a plenty of work to provide different methods to solve this problem (see [6,9,10,12,13,16,17,18,20,23,26,27]).…”

Nakayama Automorphisms of Ore Extensions Over Polynomial Algebras

“…In general, Nakayama automorphisms are known to be tough to compute. We refer to [1], [2], [3], [8], [10], [11], [13], [14], [15], [16] and the references therein for the progress on this topic during the past years.…”

On homological smoothness of generalized Weyl algebras over polynomial algebras in two variables

“…From an algebraic point of view, noncommutative rings are more rigid than commutative ones, namely, a commutative ring possesses "more" automorphisms and central elements than a noncommutative ring. A typical example is: if B is the generic quantum 2-plane k q [z 1 , z 2 ], then σ is necessarily given by σ(z 1 ) = az 1 , σ(z 2 ) = bz 2 for some nonzero scalars a, b ∈ k, and the central element ϕ must be in k. One concludes that in this case any generalized Weyl [34], [30], [31], [33], [40] and the references therein for the progress on this topic during the past years. The goal in §4 is to compute the Nakayama automorphism of W (2) .…”