Indecomposable characters of infinite dimensional groups associated with operator algebras. (English) Zbl 1353.22011

Enomoto, Takumi; Izumi, Masaki

J. Math. Soc. Japan 68, No. 3, 1231-1270 (2016).

The paper under review determines indecomposable characters of several classes of infinite dimensional groups associated with operator algebras. The first main result classifies the indecomposable characters for the unitary groups of arbitrary unital simple AF algebras. Using this classification, the authors obtain further classification results for broader classes of groups, in particular, for the unitary groups of arbitrary type \(\mathrm{II}_{1}\) factors and for a family of subgroups of the unitary groups of arbitrary type \(\mathrm{II}_{\infty}\) factors.

Reviewer: Volodymyr Mazorchuk (Uppsala)

MSC:

22E66	Analysis on and representations of infinite-dimensional Lie groups
46L99	Selfadjoint operator algebras (\(C^*\)-algebras, von Neumann (\(W^*\)-) algebras, etc.)

Keywords:

character; infinite dimensional group; ergodic method; AF algebra