BICOVARIANT CALCULUS ON TWISTED ISO(N), QUANTUM POINCARÉ GROUP AND QUANTUM MINKOWSKI SPACE

@article{Aschieri1996BICOVARIANTCO,
  title={BICOVARIANT CALCULUS ON TWISTED ISO(N), QUANTUM POINCAR{\'E} GROUP AND QUANTUM MINKOWSKI SPACE},
  author={Paolo Aschieri and Leonardo Castellani},
  journal={International Journal of Modern Physics A},
  year={1996},
  volume={11},
  pages={4513-4549}
}
A bicovariant calculus on the twisted inhomogeneous multiparametric q groups of the Bn, Cn, Dn types, and on the corresponding quantum planes, is found by means of a projection from the bicovariant calculus on Bn+1, Cn+1, Dn+1. In particular we obtain the bicovariant calculus on a dilatation-free q Poincare group ISOq(3, 1), and on the corresponding quantum Minkowski space. The classical limit of the Bn, Cn, Dn bicovariant calculus is discussed in detail. 
On the geometry of inhomogeneous quantum groups
The author gives a pedagogical introduction to the differential calculus on quantum groups by stressing at all stages the connection with the classical case. He further analyzes the relation between
On the Noncommutative Geometry of Twisted Spheres
We describe noncommutative geometric aspects of twisted deformations, in particular of the spheres of Connes and Landi and of Connes and Dubois Violette, by using the differential and integral
Q A ] 5 D ec 2 00 1 On the Noncommutative Geometry of Twisted Spheres
We describe noncommutative geometric aspects of twisted deformations, in particular of the spheres in Connes and Landi [8] and in Connes and Dubois Violette [7], by using the differential and
New Lie-algebraic and quadratic deformations of Minkowski space from twisted Poincaré symmetries
Abstract We consider two new classes of twisted D = 4 quantum Poincare symmetries described as the dual pairs of noncocommutative Hopf algebras. Firstly we investigate a two-parameter class of
Universal Enveloping Algebra and differential calculi on inhomogeneous orthogonal q-groups
We review the construction of the multiparametric quantum group ISOq,r(N) as a projection from SOq,r (N + 2) and show that it is a bicovariant bimodule over SOq,r(N). The universal enveloping algebra
Geometrical Tools for Quantum Euclidean Spaces
Abstract: We apply one of the formalisms of noncommutative geometry to ℝNq, the quantum space covariant under the quantum group SOq(N). Over ℝNq there are two SOq(N)-covariant differential calculi.
FRAME FORMALISM FOR THE N-DIMENSIONAL QUANTUM EUCLIDEAN SPACES
We sketch our application1 of a non-commutative version of the Cartan "moving-frame" formalism to the quantum Euclidean space the space which is covariant under the action of the quantum group
Communications in Mathematical Physics Noncommutative Instantons from Twisted Conformal Symmetries
We construct a five-parameter family of gauge-nonequivalent SU (2) instantons on a noncommutative four sphere S4 θ and of topological charge equal to 1. These instantons are critical points of a
Hopf Algebras in Noncommutative Geometry
We give an introductory survey to the use of Hopf algebras in several problems of noncommutative geometry. The main example, the Hopf algebra of rooted trees, is a graded, connected Hopf algebra
Metrics on the real quantum plane
Using the frame formalism we determine some possible metrics and metric-compatible connections on the noncommutative differential geometry of the real quantum plane. By definition, a metric maps the
...
1
2
3
4
...

References

SHOWING 1-10 OF 26 REFERENCES
Inhomogeneous quantum groups IGL-q,r(N): Universal enveloping algebra and differential calculus
A review of the multiparametric linear quantum group GLq,r(N), its real forms, its dual algebra U[glq,r(N)] and its bicovariant differential calculus is given in the first part of the paper. We then
Universal Enveloping Algebra and differential calculi on inhomogeneous orthogonal q-groups
We review the construction of the multiparametric quantum group ISOq,r(N) as a projection from SOq,r (N + 2) and show that it is a bicovariant bimodule over SOq,r(N). The universal enveloping algebra
SOq(n+1,n−1) as a real form of SOq(2n,ℂ)
Quantum pseudo-orthogonal groups SOq(n+1,n−1) are defined as real forms of quantum orthogonal groups SOq(n+1,n−1) by means of a suitable antilinear involution. In particular, the casen=2 gives a
Vector Fields on Quantum Groups
We construct the space of vector fields on a generic quantum group. Its elements are products of elements of the quantum group itself with left-invariant vector fields. We study the duality between
Matrix formulation of the quantum inhomogeneous groups ISO q,r (N) and ISp q
  • Matrix formulation of the quantum inhomogeneous groups ISO q,r (N) and ISp q
Commun. Math. Phys
  • Commun. Math. Phys
  • 1994
J. Phys
  • J. Phys
  • 1991
N. Reshetikhin, Lett. Math. Phys
  • N. Reshetikhin, Lett. Math. Phys
  • 1990
233 (contains the first part of the unpublished preprint On the quantum Poincaré group
  • Math. Phys
  • 1994
233 (contains the first part of the unpublished preprint On the quantum Poincaré group
  • Math. Phys
  • 1994
...
1
2
3
...