The multiparametric deformation ofGL(n) and the covariant differential calculus on the quantum vector space

Differential calculus on the quantum superspace and deformation of phase space

“…Note that for the case of GL(2|0) (GL(n|0)), (2.20) reduces to the well-known result forR-matrix of the 2-parameter (the multiparameter) deformation of GL (2) [11] (GL(n) [12,13]). (The multiparameter deformation of GL(n) was also considered in ref.…”

“…We now extend the differential calculus on quantum space developed by Wess and Zumino [10] and others [11][12][13][14] to this quantum superspace. Here we require that the exterior derivative d given by…”

“…Woronowicz has initiated the differential calculus on the non-commutative space of quantum groups [8], which provides an example for non-commutative differential geometry [9]. Wess and Zumino and others developed the differential calculus on the quantum (hyper-)plane covariant with respect to quantum groups [10] and multiparameter deformation of the quantum groups, especially for GL q (n) [11,12,13], as well as for SO q (n) [14]. Now it would be interesting to study q-deformation of supergroups from the viewpoint of quantum space.…”

The inhomogeneous quantum invariance group of commuting fermions

“…This determinant can also be found by starting from the rule which has been constructed to calculate the determinant in GL p,q (d) [12]. In the ordinary determinant rule the sign factor is an tensor.…”

THERMODYNAMIC PROPERTIES OF A QUANTUM GROUP BOSON GAS GLp,q(2)

“…In effect, we would like to establish a set of the background useful in the next, which leads to obtain a quantum group bosons. For this matter, we start by recalling GL p ij ,q ij (N), i, j = 1, ..., N. The latter is defined by the commutation relations [21] …”