Representations of Cuntz algebras, loop groups and wavelets
摘要
A theorem of Glimm states that representation theory of an NGCR C*-algebra is always intractable, and the Cuntz algebra O_N is a case in point. The equivalence classes of irreducible representations under unitary equivalence cannot be captured with a Borel cross section. Nonetheless, we prove here that wavelet representations correspond to equivalence classes of irreducible representations of O_N, and they are effectively labeled by elements of the loop group, i.e., the group of measurable functions A:T-->U_N(C). These representations of O_N are constructed here from an orbit picture analysis of the infinite-dimensional loop group.
引用
@article{arxiv.math/0008102,
title = {Representations of Cuntz algebras, loop groups and wavelets},
author = {Palle E. T. Jorgensen},
journal= {arXiv preprint arXiv:math/0008102},
year = {2007}
}
备注
6 pages, LaTeX2e "amsproc" class; expanded version of an invited lecture given by the author at the International Congress on Mathematical Physics, July 2000 in London