Yoneda Ext-algebras of Takeuchi smash products

TL;DR

This paper establishes a fundamental relationship between the Yoneda Ext-algebras of Takeuchi smash products and their factors, demonstrating preservation of Artin-Schelter regularity and detailing the Nakayama automorphism.

Contribution

It proves that the Yoneda Ext-algebra of a Takeuchi smash product equals the graded Takeuchi smash product of the individual Ext-algebras, a novel structural result.

Findings

Yoneda Ext-algebra of a Takeuchi smash product equals the graded Takeuchi smash product of the factors' Ext-algebras

Graded Takeuchi smash products preserve Artin-Schelter regularity

The Nakayama automorphism of the product is explicitly described

Abstract

We prove that the Yoneda Ext-algebra of a Takeuchi smash product is the graded Takeuchi smash product of the Yoneda Ext-algebras of the two algebras or modules involved. As an application, we prove that graded Takeuchi smash products preserve Artin-Schelter regularity, and describe the Nakayama automorphism of the product.