Mathematics – Quantum Algebra
Scientific paper
1996-02-07
From field theory to quantum groups, B. Jancewicz and J. Sobczyk eds., pp. 3-27, World Sci. 1996
Mathematics
Quantum Algebra
TeX file, 25 pages. Macros are included
Scientific paper
We re-examine all the contractions related with the ${\cal U}_q(su(2))$ deformed algebra and study the consequences that the contraction process has for their structure. We also show using ${\cal U}_q(su(2))\times{\cal U}(u(1))$ 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.
de Azcarraga Jose A.
Perez Bueno J. C.
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