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Equivariant Morita equivalences between Podleś spheres

100%

De Commer K.

Banach Center Publications

2012

tom 98

nr 1

85-105

We show that the family of Podleś spheres is complete under equivariant Morita equivalence (with respect to the action of quantum SU(2)), and determine the associated orbits. We also give explicit formulas for the actions which are equivariantly Morita equivalent with the quantum projective plane. In both cases, the computations are made by examining the localized spectral decomposition of a generalized Casimir element.

Poisson-Lie groupoids and the contraction procedure

100%

De Commer K.

Banach Center Publications

2015

tom 106

nr 1

35-46

On the level of Lie algebras, the contraction procedure is a method to create a new Lie algebra from a given Lie algebra by rescaling generators and letting the scaling parameter tend to zero. One of the most well-known examples is the contraction from 𝔰𝔲(2) to 𝔢(2), the Lie algebra of upper-triangular matrices with zero trace and purely imaginary diagonal. In this paper, we will consider an extension of this contraction by taking also into consideration the natural bialgebra structures on these Lie algebras. This will give a bundle of central extensions of the above Lie algebras with a Lie bialgebroid structure having transversal component. We consider as well the dual Lie bialgebroid, which is in a sense easier to understand, and whose integration can be explicitly presented.

Ograniczanie wyników

2 Banach Center Publications

2 De Commer K.

1 2015

1 2012

Wyniki wyszukiwania

Equivariant Morita equivalences between Podleś spheres

Poisson-Lie groupoids and the contraction procedure