# Journal of Operator Theory

Volume 82, Issue 1, Summer 2019  pp. 147-172.

Metaplectic transformations and finite group actions on noncommutative tori

Authors:  Sayan Chakraborty (1), Franz Luef (2)
Author institution:(1) Stat-Math unit, Indian Statistical Institute, 203 Barrackpore Trunk Road, Kolkata 700 108, India
(2) Department of Mathematical Sciences, NTNU Trondheim, 7041 Trondheim, Norway

Summary: In this article we describe extensions of some $\mathrm{K}$-theory classes of Heisenberg modules over higher-dimensional noncommutative tori to projective modules over crossed products of non\-commutative tori by finite cyclic groups, aka noncommutative orbifolds. The two dimensional case was treated by Echterhoff, L\"uck, Phillips and Walters. Our approach is based on the theory of metaplectic transformations of the representation theory of the Heisenberg group. We also describe the generators of the K-groups of the crossed products of flip actions by $\mathbb{Z}_2$ on 3-dimensional noncommu\-tative tori.

DOI: http://dx.doi.org/10.7900/jot.2018apr06.2220
Keywords: metaplectic transformations, noncommutative torus, $C^*$-crossed product, group actions