Blends and Alloys

TL;DR

This paper investigates how to define algebra or C*-algebra structures on tensor products of two algebras, especially when B is two-dimensional, using group actions and examples related to commuting squares.

Contribution

It characterizes all possible C*-algebra structures on tensor products with a two-dimensional algebra B using Z_2 actions, expanding understanding of algebraic tensor products.

Findings

Classifies C*-algebra structures on tensor products with B two-dimensional

Uses Z_2 group actions to describe structures

Provides an example related to commuting squares

Abstract

Given two algebras A and B, sometimes assumed to be C*-algebras, we consider the question of putting algebra or C*-algebra structures on the tensor product A\otimes B. In the C*-case, assuming B to be two-dimensonal, we characterize all possible such C*-algebra structures in terms of an action of the cyclic group Z_2. An example related to commuting squares is also discussed.