Journal article
Iterated function systems and permutation representations of the Cuntz algebra
Memoirs of the American Mathematical Society, Vol.139(663), pp.1-88
1999
DOI: 10.1090/memo/0663
Abstract
We study a class of representations of the Cuntz algebras ON, N = 2,3,..., acting on L 2 (T) where T = R 2Z. The representations arise in wavelet theory, but are of independent interest. We find and describe the decomposition into irreducibles, and show how the ON-irreducibles decompose when restricted to the subalgebra UHFNON of gauge-invariant elements; and we show that the whole structure is accounted for by arithmetic and combinatorial properties of the integers Z. We have general results on a class of representations of ON on Hilbert space H such that the generators Si as operators permute the elements in some orthonormal basis for H. We then use this to extend our results from L 2 (T) to L 2 T d , d > 1; even to L 2 (T) where T is some fractal version of the torus which carries more of the algebraic information encoded in our representations.
Details
- Title: Subtitle
- Iterated function systems and permutation representations of the Cuntz algebra
- Creators
- Ola BratteliPalle E.T Jorgensen
- Resource Type
- Journal article
- Publication Details
- Memoirs of the American Mathematical Society, Vol.139(663), pp.1-88
- DOI
- 10.1090/memo/0663
- ISSN
- 0065-9266
- eISSN
- 1947-6221
- Language
- English
- Date published
- 1999
- Academic Unit
- Mathematics
- Record Identifier
- 9983985824502771
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