Constructions of exotic group \(C^\ast\)-algebras. (English) Zbl 1373.22014

Wiersma, Matthew

Ill. J. Math. 60, No. 3-4, 655-667 (2016).

Summary: Let \(\Gamma\) be a discrete group. When \(\Gamma\) is nonamenable, the reduced and full group \(C^\ast\)-algebras differ and it is generally believed that there should be many intermediate \(C^\ast\)-algebras, however few examples are known. In this paper, we give new constructions and compare existing constructions of intermediate group \(C^\ast\)-algebras for both generic and specific groups \(\Gamma\).

MSC:

22D25	\(C^*\)-algebras and \(W^*\)-algebras in relation to group representations
22D10	Unitary representations of locally compact groups
43A35	Positive definite functions on groups, semigroups, etc.
46L05	General theory of \(C^*\)-algebras