Differential Calculus on the Quantum Superspace and Deformation of Phase Space

الأصل · EN

We investigate non-commutative differential calculus on the supersymmetric version of quantum space where the non-commuting super-coordinates consist of bosonic as well as fermionic (Grassmann) coordinates. Multi-parametric quantum deformation of the general linear supergroup, GLq(m|n), is studied and the explicit form for the R-matrix, which is the solution of the Yang-Baxter equation, is presented. We derive the quantum-matrix commutation relation of GLq(m|n) and the quantum superdeterminant. We apply these results for the GLq(m|n) to the deformed phase-space of supercoordinates and their momenta, from which we construct the R-matrix of q-deformed orthosymplectic group OSpq(2n|2m) and calculate its R-matrix. Some detailed argument for quantum super-Clifford algebras and the explict expression of the R-matrix will be presented for the case of OSpq(2|2).