Frobenius C*-algebras and local adjunctions of C*-correspondences

TL;DR

This paper introduces Frobenius C*-algebras and establishes a one-to-one correspondence with local adjunctions of C*-correspondences, extending the classical link between adjunctions and Frobenius algebras into the C*-algebraic setting.

Contribution

It defines Frobenius C*-algebras and proves their equivalence with local adjunctions of C*-correspondences, generalizing known algebraic correspondences.

Findings

Frobenius C*-algebras are introduced as a natural C*-algebraic analogue.

A one-to-one correspondence between Frobenius C*-algebras and local adjunctions is established.

The work extends classical algebraic concepts into the C*-algebra framework.

Abstract

Generalising the well-known correspondence between two-sided adjunctions and Frobenius algebras, we establish a one-to-one correspondence between local adjunctions of C*-correspondences, as defined and studied in prior work with P. Clare and N. Higson; and Frobenius C*-algebras, a natural C*-algebraic adaptation of the standard notion of Frobenius algebras that we introduce here.