Contractions, Hopf algebra extensions and cov. differential calculus

Abstract

We re-examine all the contractions related with the ${\mathcal{U}}_q(su(2))$ deformed algebra and study the consequences that the contraction process has for their structure. We also show using ${\mathcal{U}}_q(su(2))\times \mathcal{U}(u(1))$ as an example that, as in the undeformed case, the contraction may generate Hopf algebra cohomology. We shall show that most of the different Hopf algebra deformations obtained have a bicrossproduct or a cocycle bicrossproduct structure, for which we shall also give their dual `group' versions. The bicovariant differential calculi on the deformed spaces associated with the contracted algebras and the requirements for their existence are examined as well.

arXiv commentTeX file, 25 pages. Macros are included

Cited by in corpus (2)

• Canonical and Lie-algebraic twist deformations of Galilei algebra
• On the bicrossproduct structures for the ${\mathcal{U}}_{\lambda }(is{o}_{{\omega }_2...{\omega }_N}(N))$ family of algebras