A reciprocity theorem of Robinson-Benson-Webb for finite-dimensional symmetric algebras

TL;DR

This paper extends a classical reciprocity theorem from finite groups to finite-dimensional symmetric algebras connected by bimodules, broadening its applicability.

Contribution

It generalizes Robinson-Benson-Webb reciprocity to symmetric algebras via bimodule connections, a novel theoretical advancement.

Findings

Established a reciprocity relation for symmetric algebras

Extended classical group-theoretic results to algebraic structures

Provided a framework for bimodule-based algebraic reciprocity

Abstract

We generalize the reciprocity theorem of G.R.~Robinson, D. Benson and P. Webb between a finite group and its subgroup to the case of finite-dimensional {\it symmetric} algebras over a field which are connected by a bimodule for the two algebras.