Chains of extended Jordanian twists for Lie superalgebras

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.

LaTeX, 10 pages

Cited by in corpus (6)

• Target space supergeometry of $\eta$ and $\lambda$-deformed strings
• A Jordanian deformation of AdS space in type IIB supergravity
• $\kappa$-Minkowski Spacetimes and DSR Algebras: Fresh Look and Old Problems
• Yang-Baxter deformations of the Principal Chiral Model plus Wess-Zumino term
• Twisted Quantum Deformations of Lorentz and Poincaré algebras
• New twisted quantum deformations of D=4 super-Poincare algebra