Rieffel deformation via crossed products
Abstract
We start from Rieffel data (A,f,X) where A is a C*algebra, X is an action of an abelian group H on A and f is a 2cocycle on the dual group. Using Landstad theory of crossed product we get a deformed C*algebra A(f). In the case of H being the nth Cartesian product of the real numbers we obtain a very simple proof of invariance of Kgroups under the deformation. In the general case we also get a very simple proof that nuclearity is preserved under the deformation. We show how our approach leads to quantum groups and investigate their duality. The general theory is illustrated by an example of the deformation of SL(2,C). A description of it, in terms of noncommutative coordinates is given.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 2006
 arXiv:
 arXiv:math/0606333
 Bibcode:
 2006math......6333K
 Keywords:

 Mathematics  Operator Algebras;
 Mathematics  Quantum Algebra;
 46L89 (Primary) 58B32;
 22D25 (Secondary)
 EPrint:
 39 pages