On Combined Standard-Nonstandard or Hybrid (q,h)-Deformations

B. L. Aneva , D. Arnaudon (1) , A. Chakrabarti (2) , V. K. Dobrev , S. G. Mihov

1 LAPTH - Laboratoire d'Annecy-le-Vieux de Physique Théorique
2 CPHT - Centre de Physique Théorique [Palaiseau]

Combined $(q,h)$-deformations proposed by Kupershmidt and Ballesteros-Herranz-Parashar are studied. In each case a transformation is shown to lead to an equivalent, standard $q$-deformation. We briefly indicate that appropriate singular limits of the same type of transformations can however lead from standard biparametric $(p,q)$-deformations to non-hybrid but biparametric nonstandard $(g,h)$ ones. Finally a case of hybrid $(q,h)$-deformation is recalled, related to the superalgebra $GL(1|1)$.

Domaines: Algèbres quantiques [math.QA]

B. L. Aneva, D. Arnaudon, A. Chakrabarti, V. K. Dobrev, S. G. Mihov. On Combined Standard-Nonstandard or Hybrid (q,h)-Deformations. Journal of Mathematical Physics, 2001, 42, pp.1236-1249. ⟨hal-00007527⟩