Heisenberg-Weyl Representations and Morita equivalence for crossed products of Noncommutative solenoids
Abstract
We study strong Morita equivalence for crossed products of noncommutative solenoids by cyclic groups. Using their description as twisted group C*-algebras, we construct automorphisms induced by the natural linear action of SL2(ℤ[1/p]) on ℤ[1/p]2, for every integer p>1. For odd primes, we use the Heisenberg--Weyl representation to construct compatible cyclic group actions on the equivalence bimodules relating solenoids with reciprocal parameters. This yields strong Morita equivalences between the corresponding crossed products by ℤ and, for finite-order matrices, by finite cyclic groups. The corresponding equivalence for flip crossed products for the action of ℤ/2ℤ holds for every prime, including $2$. For prime p, we give representatives for the nontrivial finite subgroups of SL2(ℤ[1/p]) and explicit arithmetic criteria for conjugacy among these representatives.
Related
- Equivariant Morita equivalence for finite cyclic group actions on noncommutative tori
- Induced representations from the Heisenberg parabolic subgroup of SL(n+2,ℝ)
- Facets of nondegeneracy: central type factor groups, Heisenberg representations and Hadamard matrices
- From Common-Slot Chains to Heisenberg Central Products over Global Fields
- Central Haagerup Tensor Products and Completely Bounded Maps under Strong Morita Equivalence
BibTeX
@misc{kundu2026heisenbergweyl,
title = {{Heisenberg-Weyl Representations and Morita equivalence for crossed products of Noncommutative solenoids}},
author = {Pratik Kumar Kundu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.03353},
eprint = {2607.03353},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.03353},
}
RIS
TY - UNPB
TI - Heisenberg-Weyl Representations and Morita equivalence for crossed products of Noncommutative solenoids
AU - Pratik Kumar Kundu
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2607.03353
UR - https://arxiv.org/abs/2607.03353
AB - We study strong Morita equivalence for crossed products of noncommutative solenoids by cyclic groups. Using their description as twisted group C^*-algebras, we construct automorphisms induced by the natural linear action of SL_2(ℤ[1/p]) on ℤ[1/p]^2, for every integer p>1. For odd primes, we use the Heisenberg--Weyl representation to construct compatible cyclic group actions on the equivalence bimodules relating solenoids with reciprocal parameters. This yields strong Morita equivalences between the corresponding crossed products by ℤ and, for finite-order matrices, by finite cyclic groups. The corresponding equivalence for flip crossed products for the action of ℤ/2ℤ holds for every prime, including $2$. For prime p, we give representatives for the nontrivial finite subgroups of SL_2(ℤ[1/p]) and explicit arithmetic criteria for conjugacy among these representatives.
ER -