Dg analogues of the Zuckerman functors and the dual Zuckerman functors I

TL;DR

This paper develops differential graded (dg) analogues of key functors in the theory of Harish-Chandra modules, expanding the algebraic toolkit for representation theory over arbitrary rings.

Contribution

It introduces dg versions of the induction, production, Zuckerman, and dual Zuckerman functors for dg Harish-Chandra modules, a novel extension of classical concepts.

Findings

Constructed dg analogues of classical functors

Applicable to modules over arbitrary commutative rings

Provides new tools for dg representation theory

Abstract

We study the category of dg Harish-Chandra modules (over an arbitrary commutative ring) and construct dg analogues of the induction functor, the production functor, the Zuckerman functor and the dual Zuckerman functor.