Two-parametric extension of \(h\)-deformation of \(\text{Gr}(1|1)\). (English) Zbl 0961.81032
Summary: The two-parametric quantum deformation of the algebra of coordinate functions on the (dual) supergroup \(\text{Gr}(1\mid 1)\) via a contraction of \(\text{Gr}_{p,q} (1\mid 1)\) is presented. Although the quantum superdeterminant of any element of \(\text{Gr}_{p,q}(1\mid 1)\) is not central, in the two parametric Jordanian deformation of \(\text{Gr} (1\mid 1)\) the quantum superdeterminant belongs to the center. The Hopf algebra structure of \(\text{Gr}_{h_1,h_2} (1\mid 1)\) is discussed.
MSC:
| 81R50 | Quantum groups and related algebraic methods applied to problems in quantum theory |
| 17B37 | Quantum groups (quantized enveloping algebras) and related deformations |
Keywords:
two-parametric quantum deformation; algebra of coordinate functions; supergroup; contraction; quantum superdeterminant; two parametric Jordanian deformation; Hopf algebra structureReferences:
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