Twisted Heisenberg doubles
Quantum Algebra
2016-04-08 v2 Rings and Algebras
Representation Theory
Abstract
We introduce a twisted version of the Heisenberg double, constructed from a twisted Hopf algebra and a twisted Hopf pairing. We state a Stone--von Neumann type theorem for a natural Fock space representation of this twisted Heisenberg double and deduce the effect on the algebra of shifting the product and coproduct of the original twisted Hopf algebra. We conclude by showing that the quantum Weyl algebra, quantum Heisenberg algebras, and lattice Heisenberg algebras are all examples of the general construction.
Keywords
Cite
@article{arxiv.1405.7889,
title = {Twisted Heisenberg doubles},
author = {Daniele Rosso and Alistair Savage},
journal= {arXiv preprint arXiv:1405.7889},
year = {2016}
}
Comments
22 pages; v2: minor corrections