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Algebraic and Differential Star Products on Regular Orbits of Compact Lie Groups

2000

In this paper we study a family of algebraic deformations of regular coadjoint orbits of compact semisimple Lie groups with the Kirillov Poisson bracket. The deformations are restrictions of deformations on the dual of the Lie algebra. We prove that there are non isomorphic deformations in the family. The star products are not differential, unlike the star products considered in other approaches. We make a comparison with the differential star product canonically defined by Kontsevich's map.

High Energy Physics - TheoryGeneral MathematicsSimple Lie groupLie groupFOS: Physical sciencesRepresentation theoryLie Grups deAlgebraPoisson bracketCompact groupHigh Energy Physics - Theory (hep-th)Star productMathematics::Quantum AlgebraMathematics - Quantum AlgebraLie algebraFOS: MathematicsQuantum Algebra (math.QA)Astrophysics::Earth and Planetary AstrophysicsÀlgebraDifferential (mathematics)Mathematics
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On the Embedding of Space-Time Symmetries into Simple Superalgebras

2001

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.

High Energy Physics - TheoryHigh Energy Physics - Theory (hep-th)FOS: Physical sciencesÀlgebraLie Grups deParticle Physics - Theory
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