**Chalmers University of Technology and University of Gothenburg-
Sweden**

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

A celebrated result of Elliott states that the Cuntz algebra ๐ช_{2} is self-absorbing, in the sense that ๐ช_{2}⊗๐ช_{2}=๐ช_{2} . 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 L_{2} , which is the purely algebraic version of ๐ช_{2} , 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 ๐ช_{2}^{p} of the Cuntz algebra, as introduced and studied by Phillips. As it turns out, for p≠2 there is no isometric isomorphism between ๐ช_{2}^{p} and ๐ช_{2}^{p}⊗๐ช_{2}^{p} . Even more, in this case there is no unital, isometric embedding of ๐ช_{2}^{p}⊗๐ช_{2}^{p} into ๐ช_{2}^{p}, thus also refuting an L^{p}-version of Kirchberg's embedding theorem.

This is joint work with Jan Gundelach.