Kernels of Fell bundles tensor products

TL;DR

This paper establishes a fundamental compatibility between tensor products of Fell bundle kernels and their associated C*-algebras, demonstrating that tensoring kernels aligns with tensoring the bundles themselves.

Contribution

It proves that the minimal and maximal tensor products of kernel C*-algebras correspond to the kernels of the tensor products of Fell bundles over locally compact groups.

Findings

Minimal tensor product of kernel C*-algebras equals kernel of minimal tensor product of bundles.

Maximal tensor product of kernel C*-algebras equals kernel of maximal tensor product of bundles.

Results unify tensor product operations in the context of Fell bundles and their kernels.

Abstract

We prove that if A and B are Fell bundles over the locally compact groups G and H respectively, then the minimal (maximal) tensor product of the C*-algebra of kernels of A with the C*-algebra of kernels of B agrees with the C*-algebra of kernels of the minimal (respectively: maximal) tensor product of A and B.