The $q$-calculus for generic $q$ and $q$ a root of unity

R. S. Dunne; A. J. Macfarlane; J. A. de Azcárraga; J. C. Pérez Bueno

doi:10.1007/BF01690338

The $q$-calculus for generic $q$ and $q$ a root of unity

q-alg 2009-10-30 v1 High Energy Physics - Theory Quantum Algebra

Authors: R. S. Dunne , A. J. Macfarlane , J. A. de Azcárraga , J. C. Pérez Bueno

View on arXiv ↗ PDF ↗ DOI ↗

Abstract

The $q$ -calculus for generic $q$ is developed and related to the deformed oscillator of parameter $q^{1/2}$ . By passing with care to the limit in which $q$ is a root of unity, one uncovers the full algebraic structure of ${{\cal Z}}_n$ -graded fractional supersymmetry and its natural representation.

Keywords

q-calculus deformed oscillator roots of unity fractional supersymmetry

Cite

@article{arxiv.q-alg/9609002,
  title  = {The $q$-calculus for generic $q$ and $q$ a root of unity},
  author = {R. S. Dunne and A. J. Macfarlane and J. A. de Azcárraga and J. C. Pérez Bueno},
  journal= {arXiv preprint arXiv:q-alg/9609002},
  year   = {2009}
}

Comments

8 pages, LaTeX, submitted to Proceedings of the 5th Colloquium `Quantum groups and integrable systems', Prague, June 1996 (to appear in Czech. J. Phys.)

The $q$-calculus for generic $q$ and $q$ a root of unity

Abstract

Keywords

Cite

Comments

Related papers