Analysis on discrete cocompact subgroups of the generic filiform Lie groups

Kamran Reihani; Paul Milnes

doi:10.1007/s10474-006-0059-z

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Acta Mathematica Hungarica

Volume/Issue:: Volume 112: Issue 1-2

Analysis on discrete cocompact subgroups of the generic filiform Lie groups

Authors:

Kamran Reihani

Kamran Reihani Department of Mathematics, University of Oslo P.O. Box Blindern, 0316 Oslo, Norway P.O. Box Blindern, 0316 Oslo, Norway

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Paul Milnes

Paul Milnes Department of Mathematics, University of Western Ontario London, Ont. N6A 5B9, Canada London, Ont. N6A 5B9, Canada

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Pages:: 157–179

Online Publication Date:: 18 Jul 2006

Publication Date:: 18 Jul 2006

Article Category:: Research Article

DOI:: https://doi.org/10.1007/s10474-006-0059-z

Keywords:: group C*-algebra; simple quotient; C*-crossed product; filiform Lie group; discrete nilpotent group

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Summary

Let F_n, n≧ 1, denote the sequence of generic filiform (connected, simply connected) Lie groups. Here we study, for each F_n, the infinite dimensional simple quotients of the group C*-algebra of (the most obvious) one of its discrete cocompact subgroups D_n. For D_n, the most attractive concrete faithful representations are given in terms of Anzai flows, in analogy with the representations of the discrete Heisenberg group H₃⊆G₃ on L²(T) that result from the irrational rotation flows on T; the representations of D_n generate infinite-dimensional simple quotients A_n_,θ of the group C*-algebra C*(D_n). For n>1, there are other infinite-dimensional simple quotients of C*(D_n) arising from non-faithful representations of D_n. Flows for these are determined, and they are also characterized and represented as matrix algebras over simple affine Furstenberg transformation group C*-algebras of the lower dimensional tori.

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Acta Mathematica Hungarica

Print ISSN:: 0236-5294

Online ISSN:: 1588-2632

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Acta Mathematica Hungarica
Language	English
Size	B5
Year of Foundation	1950
Volumes per Year	3
Issues per Year	6
Founder	Magyar Tudományos Akadémia
Founder's Address	H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher	Akadémiai Kiadó Springer Nature Switzerland AG
Publisher's Address	H-1117 Budapest, Hungary 1516 Budapest, PO Box 245. CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible Publisher	Chief Executive Officer, Akadémiai Kiadó
ISSN	0236-5294 (Print)
ISSN	1588-2632 (Online)