Generalization and Deformations of Quantum Groups; Quantization of All Simple Lie Bi-Algebras

Details Generalization and Deformations of Quantum Groups; Quantization of All Simple Lie Bi-Algebras Generalization and Deformations of Quantum Groups; Quantization of All Simple Lie Bi-Algebras

1995-10-02

arxiv.org/abs/q-alg/9510002v1

Mathematics

Quantum Algebra

35 pages

Scientific paper

A large family of "standard" coboundary Hopf algebras is investigated. The existence of a universal R-matrix is demonstrated for the case when the parameters are in general position. Special values of the parameters are characterized by the appearance of certain ideals; in this case the universal R-matrix exists on the associated algebraic quotient. In special cases the quotient is a "standard" quantum group; all familiar quantum groups including twisted ones are obtained in this way. In other special cases one finds new types of coboundary bi-algebras. A large class of first order deformations of all these standard bi-algebras is investigated and the associated deformed universal R-matrices have been calculated. One obtains, in particular, universal R-matrices associated with all simple, complex Lie algebras (classification by Belavin and Drinfeld) to first order in the deformation parameter.

Affiliated with

Also associated with

No associations

Rating

Generalization and Deformations of Quantum Groups; Quantization of All Simple Lie Bi-Algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Generalization and Deformations of Quantum Groups; Quantization of All Simple Lie Bi-Algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Generalization and Deformations of Quantum Groups; Quantization of All Simple Lie Bi-Algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-211230