2 research outputs found
Kappa-Minkowski spacetime, Kappa-Poincar\'{e} Hopf algebra and realizations
We unify kappa-Minkowki spacetime and Lorentz algebra in unique Lie algebra.
Introducing commutative momenta, a family of kappa-deformed Heisenberg algebras
and kappa-deformed Poincare algebras are defined. They are specified by the
matrix depending on momenta. We construct all such matrices. Realizations and
star product are defined and analyzed in general and specially, their relation
to coproduct of momenta is pointed out. Hopf algebra of the Poincare algebra,
related to the covariant realization, is presented in unified covariant form.
Left-right dual realizations and dual algebra are introduced and considered.
The generalized involution and the star inner product are analyzed and their
properties are discussed. Partial integration and deformed trace property are
obtained in general. The translation invariance of the star product is pointed
out. Finally, perturbative approach up to the first order in is presented
in Appendix.Comment: references added, typos corrected, acceped in J. Phys.
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