Symmetrized non-commutative tori

Metaplectic transformations and finite group actions on noncommutative tori

“…Using this result, for totally irrational θ (for definition see 7.2), we discuss the K-theory of crossed products of 3-dimensional A θ with respect to the flip action and describe the generators of K-theory (see Corollary 7.2). This explains the computations of [7] for the three dimensional case (for totally irrational θ). Presumably this can be done as well for the n-dimensional case, which we plan to discuss in another paper.…”

The structure of higher-dimensional noncommutative tori and metric diophantine approximation.

“…In this section we extend the theorem of Bratteli and Kishimoto ( [9]) and the result from [6] to the case N i> 3 and obtain the following Statement, which provides a partial answer to a natural question raised in [24]: We prove by induction on 7V ^ 2 that j/J^ has Lebesgue measure 1. For N -2, j/J^ = 7\Q (cf.…”

“…Noncommutative tori are endowed with a natural order two automorphism σ, called the flip and arising from the group automorphism g -» -g of Z N ( [8], [30], [9], [24], [42], [6]). For all N 2> 3, the set {0 = (e jk ) l^j<k^N \A e is inductive limit of direct sums of2 N~i circle algebras} has Lebesgue measure one in [0,1) 2 Corollary B.…”

“…The K-groups of symmetrized noncommutative tori have been computed in [30] for N = 2 and in [24] for N ^ 3. The K-groups of symmetrized noncommutative tori have been computed in [30] for N = 2 and in [24] for N ^ 3.…”

Compactification of M(atrix) theory on noncommutative toroidal orbifolds

“…The K-groups of B θ were calculated in [21]: K 0 (B θ ) ∼ = Z 3·2 d−1 , K 1 (B θ ) = 0. One can check that the projective modules we constructed above generate the group K 0 (B θ ).…”