Speaker: Kei Hasegawa (Kyushu Univ.)

Title: Bass-Serre trees of amalgamated free product C^*-algebras

Time/Date: 4:45-6:15, Monday, April 24, 2017.

Room: 118

Abstract: It is well-known that any amalgamated free product of groups admits a natural action on its associated Bass-Serre tree. Using this action, Julg-Valette and Ozawa proved, among others, the following results, respectively:

1) Any amalgamated free product of amenable groups is "amenable in K-theory" (Julg and Valette).

2) The natural action of any amalgamated free product of amenable groups on the compactification of its Bass-Serre tree is amenable (Ozawa).

In this talk, we consider C^*-algebraic counterparts of the Bass-Serre trees for arbitrary reduced amalgamated free products of C^*-algebras, and then show analogous results of above two results.