K-groups of the quantum homogeneous space SUq(n)∕SUq(n− 2)

k - Homogeneous Groups *

Quantum Automorphism Groups of Homogeneous Graphs

Associated to a finite graph X is its quantum automorphism group G. The main problem is to compute the Poincaré series of G, meaning the series f(z) = 1 + c1z + c2z 2 + . . . whose coefficients are multiplicities of 1 into tensor powers of the fundamental representation. In this paper we find a duality between certain quantum groups and planar algebras, which leads to a planar algebra formulati...

A quantum homogeneous space of nilpotent matrices

A quantum deformation of the adjoint action of the special linear group on the variety of nilpotent matrices is introduced. New non-embedded quantum homogeneous spaces are obtained related to certain maximal coadjoint orbits, and known quantum homogeneous spaces are revisited. MSC: 16W35; 20G42; 17B37; 81R50

ISOMETRY GROUPS OF k-CURVATURE HOMOGENEOUS PSEUDO-RIEMANNIAN MANIFOLDS

We study the isometry groups of a family of complete p + 2curvature homogeneous pseudo-Riemannian metrics on R which have neutral signature (3 + 2p, 3 + 2p), and which are 0-curvature modeled on an indecomposible symmetric space.

Decoupling of Translations from Homogeneous Transformations in Inhomogeneous Quantum Groups∗

We briefly report on our result that, if there exists a realization of a Hopf algebra H in a H-module algebra A, then their cross-product is equal to the product of A itself with a subalgebra isomorphic to H and commuting with A. We illustrate its application to the Euclidean quantum groups in N ≥ 3 dimensions.