Differential calculus onISO q(N), quantum Poincaré algebra and q-gravity

Braided differential calculus and quantum Schubert calculus

We provide a new realization of the quantum cohomology ring of a flag variety as a certain commutative subalgebra in the cross product of the Nichols-Woronowicz algebras associated to a certain Yetter-Drinfeld module over the Weyl group. We also give a generalization of some recent results by Y.Bazlov to the case of the Grothendieck ring of a flag variety of classical type. Résumé. Nous fournis...

Basics of Algebra, Topology, and Differential Calculus

Multi-dimensional Virasoro algebra and quantum gravity

I review the multi-dimensional generalizations of the Virasoro algebra, i.e. the non-central Lie algebra extensions of the algebra vect(N) of general vector fields in N dimensions, and its Fock representations. Being the Noether symmetry of background independent theories such as N -dimensional general relativity, this algebra is expected to be relevant to the quantization of gravity. To this e...

Dynamical Regge Calculus as Lattice Quantum Gravity

We propose a hybrid model of simplicial quantum gravity by performing at once dynamical triangulations and Regge calculus. A motive for the hybridization is to give a dynamical description of topology-changing processes of Euclidean spacetime. In addition, lattice diffeomorphisms as invariance of the simplicial geometry are generated by certain elementary moves in the model. We attempt also a l...

Differential calculus on q - Minkowski space 1

We wish to report here on a recent approach [1] to the non-commutative calculus on q-Minkowski space which is based on the reflection equations (RE) with no spectral parameter. These are considered as the expression of the invariance (under the coaction of the q-Lorentz group) of the commutation properties which define the different q-Minkowski algebras. This approach also allows us to discuss ...