2 research outputs found
Noncommutative Differential Forms on the kappa-deformed Space
We construct a differential algebra of forms on the kappa-deformed space. For
a given realization of the noncommutative coordinates as formal power series in
the Weyl algebra we find an infinite family of one-forms and nilpotent exterior
derivatives. We derive explicit expressions for the exterior derivative and
one-forms in covariant and noncovariant realizations. We also introduce
higher-order forms and show that the exterior derivative satisfies the graded
Leibniz rule. The differential forms are generally not graded-commutative, but
they satisfy the graded Jacobi identity. We also consider the star-product of
classical differential forms. The star-product is well-defined if the
commutator between the noncommutative coordinates and one-forms is closed in
the space of one-forms alone. In addition, we show that in certain realizations
the exterior derivative acting on the star-product satisfies the undeformed
Leibniz rule.Comment: to appear in J. Phys. A: Math. Theo
Generalized kappa-deformed spaces, star-products, and their realizations
In this work we investigate generalized kappa-deformed spaces. We develop a
systematic method for constructing realizations of noncommutative (NC)
coordinates as formal power series in the Weyl algebra. All realizations are
related by a group of similarity transformations, and to each realization we
associate a unique ordering prescription. Generalized derivatives, the Leibniz
rule and coproduct, as well as the star-product are found in all realizations.
The star-product and Drinfel'd twist operator are given in terms of the
coproduct, and the twist operator is derived explicitly in special
realizations. The theory is applied to a Nappi-Witten type of NC space