Hopf-cyclic homology with contramodule coefficients

TL;DR

This paper introduces a novel class of coefficients called stable anti-Yetter-Drinfeld contramodules for Hopf-cyclic homology, expanding the algebraic tools available for studying module algebras and coalgebras.

Contribution

It defines and explores the properties of stable anti-Yetter-Drinfeld contramodules, a new type of coefficients for Hopf-cyclic homology, combining module and contramodule structures.

Findings

Defines stable anti-Yetter-Drinfeld contramodules

Establishes compatibility conditions for these coefficients

Provides foundational framework for future applications

Abstract

A new class of coefficients for the Hopf-cyclic homology of module algebras and coalgebras is introduced. These coefficients, termed stable anti-Yetter-Drinfeld contramodules, are both modules and contramodules of a Hopf algebra that satisfy certain compatibility conditions.