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- W4301155576 abstract "Let p be prime. A noncommutative p-solenoid is the C*-algebra of Z[1/p] x Z[1/p] twisted by a multiplier of that group, where Z[1/p] is the additive subgroup of the field Q of rational numbers whose denominators are powers of p. In this paper, we survey our classification of these C*-algebras up to *-isomorphism in terms of the multipliers on Z[1/p], using techniques from noncommutative topology. Our work relies in part on writing these C*-algebras as direct limits of rotation algebras, i.e. twisted group C*-algebras of the group Z^2 thereby providing a mean for computing the K-theory of the noncommutative solenoids, as well as the range of the trace on the K_0 groups. We also establish a necessary and sufficient condition for the simplicity of the noncommutative solenoids. Then, using the computation of the trace on K_0, we discuss two different ways of constructing projective modules over the noncommutative solenoids." @default.
- W4301155576 created "2022-10-04" @default.
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- W4301155576 date "2013-11-05" @default.
- W4301155576 modified "2023-09-27" @default.
- W4301155576 title "Noncommutative solenoids and their projective modules" @default.
- W4301155576 doi "https://doi.org/10.48550/arxiv.1311.1193" @default.
- W4301155576 hasPublicationYear "2013" @default.
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