%0 Generic %1 Majid1993a %A Majid, Shahn %D 1993 %K algebra braids hopf lie quandles yang-baxter %T Solutions Of The Yang-baxter Equations From Braided-Lie Algebras And Braided Groups %U http://arxiv.org/abs/hep-th/9312140 %X We obtain an R-matrix or matrix representation of the Artin braid group acting in a canonical way on the vector space of every (super)-Lie algebra or braided-Lie algebra. The same result applies for every (super)-Hopf algebra or braided-Hopf algebra. We recover some known representations such as those associated to racks. We also obtain new representations such as a non-trivial one on the ring $kx$ of polynomials in one variable, regarded as a braided-line. Representations of the extended Artin braid group for braids in the complement of $S^1$ are also obtained by the same method.

@misc{Majid1993a, abstract = { We obtain an R-matrix or matrix representation of the Artin braid group acting in a canonical way on the vector space of every (super)-Lie algebra or braided-Lie algebra. The same result applies for every (super)-Hopf algebra or braided-Hopf algebra. We recover some known representations such as those associated to racks. We also obtain new representations such as a non-trivial one on the ring $k[x]$ of polynomials in one variable, regarded as a braided-line. Representations of the extended Artin braid group for braids in the complement of $S^1$ are also obtained by the same method. }, added-at = {2009-05-22T16:55:49.000+0200}, author = {Majid, Shahn}, biburl = {https://www.bibsonomy.org/bibtex/2832c37894a1d817f9e787bc3c3492947/njj}, description = {Solutions Of The Yang-baxter Equations From Braided-Lie Algebras And Braided Groups}, interhash = {fb8edfd11db4b49169a2fadf1756eb23}, intrahash = {832c37894a1d817f9e787bc3c3492947}, keywords = {algebra braids hopf lie quandles yang-baxter}, note = {cite arxiv:hep-th/9312140 Comment: 29 pages}, timestamp = {2009-05-22T17:04:01.000+0200}, title = {Solutions Of The Yang-baxter Equations From Braided-Lie Algebras And Braided Groups}, url = {http://arxiv.org/abs/hep-th/9312140}, year = 1993 }