Yoneda Ext-algebras of Takeuchi smash products
Quanshui Wu, Ruipeng Zhu

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.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Rings, Modules, and Algebras · Commutative Algebra and Its Applications
