Nakayama automorphisms of twisted tensor products

Abstract

In this paper, we study homological properties of twisted tensor products of connected graded algebras. We focus on the Ext-algebras of twisted tensor products with a certain form of twisting maps firstly. We show those Ext-algebras are also twisted tensor products, and depict the twisting maps for such Ext-algebras indepth. With those preparations, we describe Nakayama automorphisms of twisted tensor products of noetherian Artin-Schelter regular algebras.

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

“…It is natural to ask what λ and b are. Restricted on graded Ore extensions, Zhu, Van Oystaeyen and Zhang showed λ = hdet(σ) if A is Koszul Artin-Schelter regular in [27], and Zhou, Lu and the first named author showed the same equality if A is noetherian Artin-Schelter regular generated in degree 1 in [20], where hdet is the homological determinant introduced by Jørgensen and Zhang (see [8]).…”

“…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]).…”

Algunos tipos especiales de determinantes en extensiones PBW torcidas graduadas

“…In [16] the homological determinant was defined and used to study the Artin-Schelter regular property of some algebras. Shen et al, [34] and Wu et al, [41] gave equivalent definitions of the homological determinant and established connections between homological determinant and the usual determinant. On the other hand, Nakayama automorphism plays an important role in noncommutative algebraic geometry (see Reyes et al, [27]) and its computation is not easy in the general case.…”

“…On the other hand, Nakayama automorphism plays an important role in noncommutative algebraic geometry (see Reyes et al, [27]) and its computation is not easy in the general case. Some authors have computed and studied this automorphism for special types of algebras, see for example [22,23,24,27,33,34,39,45]. The remarkable fact is the relationship between both notions, see Reyes et al, [27], Shen et al, [34] and Zhun et al, [45], for more details.…”

“…Some authors have computed and studied this automorphism for special types of algebras, see for example [22,23,24,27,33,34,39,45]. The remarkable fact is the relationship between both notions, see Reyes et al, [27], Shen et al, [34] and Zhun et al, [45], for more details. Double Ore extensions, denoted by A = R P [x 1 , x 2 ; σ, δ, τ ], were defined by Zhang and Zhang [43] where they proved that a connected graded double Ore extension of an Artin-Schelter regular algebra is Artin-Schelter regular.…”