Metaplectic transformations and finite group actions on noncommutative\n tori

2017/05/31 by Sayan Chakraborty, Chakraborty, Sayan, Franz Luef +1 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #K-Theory and Homology (math.KT) #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1705.11194

openalex publication_date 2017/05/31 · openalex created_date 2022/10/02 · openalex updated_date 2026/08/01

Abstract

In this article we describe extensions of some K-theory classes of Heisenberg\nmodules over higher-dimensional noncommutative tori to projective modules over\ncrossed products of noncommutative tori by finite cyclic groups, aka\nnoncommutative orbifolds. The two dimensional case was treated by Echterhoff,\nL "uck, Phillips and Walters. Our approach is based on the theory of\nmetaplectic transformations of the representation theory of the Heisenberg\ngroup. We also describe the generators of the K-groups of the crossed products\nof flip actions by \ℤ₂ on 3-dimensional noncommutative tori.\n

Citations

• Projective Modules over Higher-Dimensional Non-Commutative Tori

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