Ext-algebras of graded skew extensions

TL;DR

This paper investigates the structure of Ext-algebras in graded skew extensions, revealing that the Ext-algebra of such an extension can be expressed as an R-smash product of the original Ext-algebra and that of a polynomial algebra.

Contribution

It demonstrates that the Ext-algebra of a graded skew extension is an R-smash product of the Ext-algebra of the base algebra and the polynomial algebra, providing a new structural insight.

Findings

Ext-algebra of graded skew extension is an R-smash product

Yoneda product analyzed for these extensions

Structural description of Ext-algebras obtained

Abstract

In this paper, we study the Ext-algebras of graded skew extensions. For a connected graded algebra $A$ and a graded automorphism $\sigma$, we analyze the Yoneda product of the Ext-algebra of graded skew extension $A[z;\sigma]$, and prove this Ext-algebra is an $R$-smash product of the Ext-algebra of $A$ and the one of polynomial algebra $k[z]$ as an associative algebra.