Calabi-Yau structures for multiplicative preprojective algebras

TL;DR

This paper explores Calabi-Yau structures in the context of deformed multiplicative preprojective algebras, providing algebraic descriptions and proving key results on cyclic lifts for Hochschild classes.

Contribution

It introduces a concrete algebraic framework for Calabi-Yau structures on these algebras and proves a general existence and uniqueness result for negative cyclic lifts.

Findings

Established algebraic descriptions of Calabi-Yau structures

Proved existence and uniqueness of negative cyclic lifts for Hochschild classes

Advanced understanding of deformed multiplicative preprojective algebras

Abstract

In this paper we deal with Calabi-Yau structures associated with (differential graded versions of) deformed multiplicative preprojective algebras, of which we provide concrete algebraic descriptions. Along the way, we prove a general result that states the existence and uniqueness of negative cyclic lifts for non-degenerate relative Hochschild classes.