Deformation Quantization of Non Regular Orbits of Compact Lie Groups

In this paper we construct a deformation quantization of the algebra of polynomials of an arbitrary (regular and non regular) coadjoint orbit of a compact semisimple Lie group. The deformed algebra is given as a quotient of the enveloping algebra by a suitable ideal.Comment: AMS-LaTeX, 14 pages. Some changes in Lemma 3.

On algebraic supergroups, coadjoint orbits and their deformations

In this paper we study algebraic supergroups and their coadjoint orbits as affine algebraic supervarieties. We find an algebraic deformation quantization of them that can be related to the fuzzy spaces of non commutative geometry.Comment: 37 pages, AMS-LaTe

Contractions of sigma models and integration of massive modes

We show how the integration of massive modes after a spontaneous symmetry breaking in a sigma model can often be interpreted as a contraction, induced by a group contraction, of the target space of the sigma model.Comment: 9 pages. Prepared for the porceedings of the 4-th International Symposium Quantum Theory and Symmetries. Varna, Bulgaria, 15-21 August 200

A Comparison between Star Products on Regular Orbits of Compact Lie Groups

In this paper an algebraic star product and differential one defined on a regular coadjoint orbit of a compact semisimple group are compared. It is proven that there is an injective algebra homomorphism between the algebra of polynomials with the algebraic star product and the algebra of differential functions with the differential star product structure.Comment: AMS-LaTeX, 19 pages. Version to appear in the Journal of Physics

On the Embedding of Space-Time Symmetries into Simple Superalgebras

We explore the embedding of Spin groups of arbitrary dimension and signature into simple superalgebras in the case of extended supersymmetry. The R-symmetry, which generically is not compact, can be chosen compact for all the cases that are congruent mod 8 to the physical conformal algebra so($D-2$,2), $D\geq 3$. An $\rm{so}(1,1)$ grading of the superalgebra is found in all cases. Central extensions of super translation algebras are studied in this framework.Comment: AMS LaTeX, 16 page

Generalized dimensional reduction of supergravity with eight supercharges

We describe some recent investigation about the structure of generic D=4,5 theories obtained by generalized dimensional reduction of D=5,6 theories with eight supercharges. We relate the Scherk-Schwarz reduction to a special class of N=2 no-scale gauged supergravities.Comment: Contribution to the proceedings of ``NathFest'' at PASCOS conference, Northeastern University, Boston, Ma, August 200

SU(2) Poisson-Lie T duality

Poisson-Lie target space duality is a framework where duality transformations are properly defined. In this letter we investigate the pair of sigma models defined by the double SO(3,1) in the Iwasawa decomposition.Comment: 12 pages, 1 figur