Modified braid equations, Baxterizations and noncommutative spaces for the quantum groups $GL_{q}(N), SO_{q}(N)$ and $Sp_{q}(N)$

Details Modified braid equations, Baxterizations and noncommutative spaces for the quantum groups $GL_{q}(N), SO_{q}(N)$ and $Sp_{q}(N)$ Modified braid equations, Baxterizations and noncommutative spaces for the quantum groups $GL_{q}(N), SO_{q}(N)$ and $Sp_{q}(N)$

2002-06-10

arxiv.org/abs/math/0206093v1

Mathematics

Quantum Algebra

33 pages

Scientific paper

Modified braid equations satisfied by generalized ${\hat R}$ matrices (for a {\em given} set of group relations obeyed by the elements of ${\sf T}$ matrices ) are constructed for q-deformed quantum groups $GL_q (N), SO_q (N)$ and $Sp_q (N)$ with arbitrary values of $N$. The Baxterization of ${\hat R}$ matrices, treated as an aspect complementary to the {\em modification} of the braid equation, is obtained for all these cases in particularly elegant forms. A new class of braid matrices is discovered for the quantum groups $SO_{q}(N)$ and $Sp_{q}(N)$. The ${\hat R}$ matrices of this class, while being distinct from restrictions of the universal ${\hat{\cal R}}$ matrix to the corresponding vector representations, satisfy the standard braid equation. The modified braid equation and the Baxterization are obtained for this new class of ${\hat R}$ matrices. Diagonalization of the generalized ${\hat R}$ matrices is studied. The diagonalizers are obtained explicitly for some lower dimensional cases in a convenient way, giving directly the eigenvalues of the corresponding ${\hat R}$ matrices. Applications of such diagonalization are then studied in the context of associated covariantly quantized noncommutative spaces.

Affiliated with

Also associated with

No associations

Rating

Modified braid equations, Baxterizations and noncommutative spaces for the quantum groups $GL_{q}(N), SO_{q}(N)$ and $Sp_{q}(N)$ 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 Modified braid equations, Baxterizations and noncommutative spaces for the quantum groups $GL_{q}(N), SO_{q}(N)$ and $Sp_{q}(N)$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Modified braid equations, Baxterizations and noncommutative spaces for the quantum groups $GL_{q}(N), SO_{q}(N)$ and $Sp_{q}(N)$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-79438