Skew Calabi-Yau property of normal extensions

TL;DR

This paper investigates how the skew Calabi-Yau property is maintained under normal extensions in graded algebras, providing new homological identities relating Nakayama automorphisms.

Contribution

It establishes that the skew Calabi-Yau property is preserved under normal extensions and derives a homological identity linking Nakayama automorphisms in this context.

Findings

Skew Calabi-Yau property preserved under normal extensions

Derived a homological identity for Nakayama automorphisms

Showed Nakayama automorphisms map regular normal elements to multiples of themselves

Abstract

We prove that the skew Calabi-Yau property is preserved under normal extension for locally finite positively graded algebras. We also obtain a homological identity which describes the relationship between the Nakayama automorphisms of skew Calabi-Yau locally finite positively graded algebras and their normal extensions. As a preliminary, we show that the Nakayama automorphisms of skew Calabi-Yau algebras always send a regular normal element to a multiple of itself by a unit.