Chains of extended Jordanian twists for Lie superalgebras
Quantum Algebra
2007-05-23 v1 Mathematical Physics
math.MP
Abstract
Two type of superization of the Jordanian r-matrix for the Lie algebra sl(2) are considered. One type is associated with the Lie superalgebra sl(1|1) and another type is associated with the orthosymplectic Lie superalgebra osp(1|2). Extended Jordanian r-matrices of maximal order are obtained for the basic complex Lie superalgebras sl(m|n) and osp(M|2n), and a general procedure for construction of corresponding chains of extended Jordanian twists is given. We also find a relation between the extended Jordanian twist and automorphism which gives trivial coproduct for a subalgebra provided the subalgebra is a kernel of the cobracket for the corresponding r-matrix.
Cite
@article{arxiv.math/0402433,
title = {Chains of extended Jordanian twists for Lie superalgebras},
author = {V. N. Tolstoy},
journal= {arXiv preprint arXiv:math/0402433},
year = {2007}
}
Comments
LaTeX, 10 pages