English

Torsion-type $q$-deformed Heisenberg algebra and its Lie polynomials

Rings and Algebras 2023-02-15 v1

Abstract

Given a scalar parameter qq, the qq-deformed Heisenberg algebra H(q)\mathcal{H}(q) is the unital associative algebra with two generators A,BA,B that satisfy the qq-deformed commutation relation ABqBA=IAB-qBA= I, where II is the multiplicative identity. For H(q)\mathcal{H}(q) of torsion-type, that is if qq is a root of unity, characterization is obtained for all the Lie polynomials in A,BA,B and basis and graded structure and commutation relations for associated Lie algebras are studied.

Keywords

Cite

@article{arxiv.1905.02156,
  title  = {Torsion-type $q$-deformed Heisenberg algebra and its Lie polynomials},
  author = {Rafael Reno S. Cantuba and Sergei Silvestrov},
  journal= {arXiv preprint arXiv:1905.02156},
  year   = {2023}
}