# 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.

## 37 Citations

On the geometry of inhomogeneous quantum groups

- Mathematics, Physics
- 1998

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

- Mathematics, Physics
- 2001

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

- 2002

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…

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- 2006

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

- Mathematics
- 1997

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

- Mathematics, Physics
- 2001

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.…

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- 2000

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

- 2007

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

- Mathematics, Physics
- 2001

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…

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- Mathematics, Physics
- 2000

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…

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