Chalmers University of Technology and University of Gothenburg- Sweden
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 Lp-version 𝒪2p of the Cuntz algebra, as introduced and studied by Phillips. As it turns out, for p≠2 there is no isometric isomorphism between 𝒪2p and 𝒪2p⊗𝒪2p . Even more, in this case there is no unital, isometric embedding of 𝒪2p⊗𝒪2p into 𝒪2p, thus also refuting an Lp-version of Kirchberg's embedding theorem.
This is joint work with Jan Gundelach.