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96 – 100 10.1006/jnth.1997.2128 . [2] Lev , V. 1997 Optimal representations by sumsets and subset sums J. Number Theory

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for finite variable fragments and complete representations , Journal of Symbolic Logic , 73 ( 2008 ), 65 – 89 . [6] Biró , B. , Non-finite axiomatizability results in algebraic logic , Journal of Symbolic Logic , 57 ( 3 ) ( 1992 ), 832 – 843

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References [1] A hmed , T. S. , Completions, Complete representations and Omitting types , in [2], 186 – 205 . [2

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. [2] C hernoff , P. R. , Representations, automorphisms, and derivations of some operator algebras , J. Funct. Anal. , 12 ( 1973 ), 275 – 289 . [3

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] Glendinning , P. Sidorov , N. 2001 Unique representations of real numbers in noninteger bases Math. Res. Lett. 8 535 – 543

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References [1] Aldous , D. J. 1981 Representations for partially exchangeable arrays of random variables J. Multivar. Anal

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10.1307/mmj/1030374676 . [3] Estermann , T. 1930 On the representations of a number as the sum of two products Proc. London Math. Soc

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Multivariate Bernstein polynomials, convexity and related shape properties Shape Preserving Representations in Computer-aided Geometric Design Nova Publishers .

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. , Applications of Modified Pell Numbers to Representations , Ulam Quart. , 3 ( 1994 ), 34 – 53 . [5] K ilic , E. and T asci , D. , The linear algebra of the Pell matrix , Bol

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Summary  

Let Fn, n≧ 1, denote the sequence of generic filiform (connected, simply connected) Lie groups. Here we study, for each Fn, the infinite dimensional simple quotients of the group C*-algebra of (the most obvious) one of its discrete cocompact subgroups Dn. For Dn, the most attractive concrete faithful representations are given in terms of Anzai flows, in analogy with the representations of the discrete Heisenberg group H 3 G 3 on L 2(T) that result from the irrational rotation flows on T; the representations of Dn generate infinite-dimensional simple quotients An of the group C*-algebra C*(Dn). For n>1, there are other infinite-dimensional simple quotients of C*(Dn) arising from non-faithful representations of Dn. 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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