1,590 research outputs found
Two-parameter differential calculus on the h-superplane
We introduce a noncommutative differential calculus on the two-parameter
-superplane via a contraction of the (p,q)-superplane. We manifestly show
that the differential calculus is covariant under
transformations. We also give a two-parameter deformation of the
(1+1)-dimensional phase space algebra.Comment: 14 page
Differential Geometry of the q-plane
Hopf algebra structure on the differential algebra of the extended -plane
is defined. An algebra of forms which is obtained from the generators of the
extended -plane is introduced and its Hopf algebra structure is given.Comment: 9 page
Two-parameter nonstandard deformation of 2x2 matrices
We introduce a two-parameter deformation of 2x2 matrices without imposing any
condition on the matrices and give the universal R-matrix of the nonstandard
quantum group which satisfies the quantum Yang-Baxter relation. Although in the
standard two-parameter deformation the quantum determinant is not central, in
the nonstandard case it is central. We note that the quantum group thus
obtained is related to the quantum supergroup by a
transformation.Comment: 10 page
Two-Parameter Differential Calculus on the h-Exterior Plane
We construct a two-parameter covariant differential calculus on the quantum
-exterior plane. We also give a deformation of the two-dimensional fermionic
phase space.Comment: 7 page
On the Differential Geometry of
The differential calculus on the quantum supergroup GL was
introduced by Schmidke {\it et al}. (1990 {\it Z. Phys. C} {\bf 48} 249). We
construct a differential calculus on the quantum supergroup GL in a
different way and we obtain its quantum superalgebra. The main structures are
derived without an R-matrix. It is seen that the found results can be written
with help of a matrix Comment: 14 page
Cartan calculi on the quantum superplane
Cartan calculi on the extended quantum superplane are given. To this end, the
noncommutative differential calculus on the extended quantum superplane is
extended by introducing inner derivations and Lie derivatives
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