Chains of extended Jordanian twists for Lie superalgebras

Moscow State University); V.N. Tolstoy (Institute of Nuclear Physics

Chains of extended Jordanian twists for Lie superalgebras

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arxiv math/0402433 v1 pith:2M5YNO6P submitted 2004-02-26 math.QA math-phmath.MP

V.N. Tolstoy (Institute of Nuclear Physics , Moscow State University) This is my paper · ORCID

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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.

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