Mathematics – Quantum Algebra
Scientific paper
2001-03-12
Mathematics
Quantum Algebra
18 pages, no figures
Scientific paper
General solutions of the $\hat{R}TT$ equation with a maximal number of free parameters in the specrtal decomposition of vector $SO_q (3)$ $\hat{R}$ matrices are implemented to construct modified braid equations (MBE). These matrices conserve the given, standard, group relations of the nine elements of T, but are not constrained to satisfy the standard braid equation (BE). Apart from q and a normalisation factor our $\hat{R}$ contains two free parameters, instead of only one such parameter for deformed unitary algebras studied in a previous paper [1] where the nonzero right hand side of the $MBE$ had a linear term proprotional to $(\hat{R}_{(12)} - \hat{R}_{(23)})$. In the present case the r.h.s. is, in general, nonliear. Several particular solutions are given (Sec.2) and the general structure is analysed (App.A). Our formulation of the problem in terms of projectors yield also two new solutions of standard (nonmodified) braid equation (Sec.2) which are further discussed (App.B). The noncommutative 3-spaces obtained by implementing such generalized $\hat{R}$ matrices are studied (Sec.3). The role of coboundary $\hat{R}$ matrices (not satisfying the standard BE) is explored. The MBE and Baxterization are presented as complementary facets of the same basic construction, namely, the general solution of $\hat{R}TT$ equation (Sec.4). A new solution is presented in this context. As a simple but remarkable particular case a nontrivial solution of BE is obtained (App.B) for q=1. This solution has no free parameter and is not obtainable by twisting the identity matrix. In the concluding remarks (Sec.5), among other points, generalisation of our results to $SO_{q}(N)$ is discussed.
No associations
LandOfFree
Modified Braid Equations for SO_q (3) and noncommutative spaces 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 for SO_q (3) and noncommutative spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Modified Braid Equations for SO_q (3) and noncommutative spaces will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-401618