Twist Deformation of the rank one Lie Superalgebra

Abstract

The Drinfeld twist is applyed to deforme the rank one orthosymplectic Lie superalgebra $osp(1|2)$. The twist element is the same as for the $sl(2)$ Lie algebra due to the embedding of the $sl(2)$ into the superalgebra $osp(1|2)$. The R-matrix has the direct sum structure in the irreducible representations of $osp(1|2)$. The dual quantum group is defined using the FRT-formalism. It includes the Jordanian quantum group $S{L}_{\xi }(2)$ as subalgebra and Grassmann generators as well.

LaTeX, 9 pages

References in corpus (2)

• Deformed Yangians and Integrable Models
• Duality for the Jordanian Matrix Quantum Group $G{L}_{g,h}(2)$

Cited by in corpus (13)

• Classification of Low Dimensional Lie Super-Bialgebras
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• Noncommutative Geometry of Super-Jordanian $OS{p}_h(2/1)$ Covariant Quantum Space
• Snyder Noncommutativity and Pseudo-Hermitian Hamiltonians from a Jordanian Twist
• Super-Jordanian Quantum Superalgebra ${\mathcal{U}}_h(osp(2/1))$
• Drinfeld twist for two-parametric deformation of gl(2) and sl(1/2)
• New Quantum Deformation of Osp(1;2)
• Deformation of orthosymplectic Lie superalgebra osp(1|2)
• Universal T-matrix, Representations of OSp_q(1/2) and Little Q-Jacobi Polynomials
• Jordanian Quantum Algebra ${\mathcal{U}}_{\mathsf{h}}(sl(N))$ via Contraction Method and Mapping
• On Drinfel'd twist deformation of the super-Virasoro algebra
• Quantum Integrability and Quantum Groups: a special issue in memory of Petr P. Kulish