Eusebio Gardella

http://www.math.chalmers.se/~gardella/

Tensor products of Lp-Cuntz algebras

A celebrated result of Elliott states that the Cuntz algebra 𝒪₂ is self-absorbing, in the sense that 𝒪₂⊗𝒪₂=𝒪₂ . This result is, among other things, a cornerstone in the Kirchberg-Phillips' classification of purely infinite, nuclear C*-algebras. The impact that Elliott's theorem had in C*-algebra theory motivated the question of whether the Leavitt algebra L₂ , which is the purely algebraic version of 𝒪₂ , also enjoys a similar self-absorption property. This was refuted by Ara and Cortiñas a bit over 10 years ago, using Hochschild cohomology. In this talk, we will discuss the analogous question for the L^p-version 𝒪₂^p of the Cuntz algebra, as introduced and studied by Phillips. As it turns out, for p≠2 there is no isometric isomorphism between 𝒪₂^p and 𝒪₂^p⊗𝒪₂^p . Even more, in this case there is no unital, isometric embedding of 𝒪₂^p⊗𝒪₂^p into 𝒪₂^p, thus also refuting an L^p-version of Kirchberg's embedding theorem.

This is joint work with Jan Gundelach.