Search results for "Super-Poincaré algebra"

showing 4 items of 4 documents

The enveloping algebra of the Lie superalgebra osp(1,2)

1990

International audience

Algebra and Number Theory[MATH.MATH-RT]Mathematics [math]/Representation Theory [math.RT]010102 general mathematicsCurrent algebraUniversal enveloping algebraLie superalgebraN = 2 superconformal algebra01 natural sciencesAffine Lie algebraSuper-Poincaré algebraGraded Lie algebraLie conformal algebra[ MATH.MATH-RT ] Mathematics [math]/Representation Theory [math.RT]Algebra0103 physical sciences010307 mathematical physics0101 mathematicsMathematics::Representation TheoryComputingMilieux_MISCELLANEOUSMathematics
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POLYNOMIAL IDENTITIES ON SUPERALGEBRAS AND ALMOST POLYNOMIAL GROWTH

2001

Let A be a superalgebra over a field of characteristic zero. In this paper we investigate the graded polynomial identities of A through the asymptotic behavior of a numerical sequence called the sequence of graded codimensions of A. Our main result says that such sequence is polynomially bounded if and only if the variety of superalgebras generated by A does not contain a list of five superalgebras consisting of a 2-dimensional algebra, the infinite dimensional Grassmann algebra and the algebra of 2 × 2 upper triangular matrices with trivial and nontrivial gradings. Our main tool is the representation theory of the symmetric group.

Filtered algebraDiscrete mathematicsPolynomialPure mathematicsAlgebra and Number TheoryAlternating polynomialDifferential graded algebraMathematics::Rings and AlgebrasTriangular matrixLie superalgebraSuperalgebraSuper-Poincaré algebraMathematicsCommunications in Algebra
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NONCOMMUTATIVE GEOMETRY AND GRADED ALGEBRAS IN ELECTROWEAK INTERACTIONS

1992

The Standard Model of Electroweak Interactions can be described by a generalized Yang-Mills field incorporating both the usual gauge bosons and the Higgs fields. The graded derivative by means of which the Yang-Mills field strength is constructed involves both a differential acting on space-time and a differential acting on an associative graded algebra of matrices. The square of the curvature for the corresponding covariant derivative yields the bosonic Lagrangian of the Standard Model. We show how to recover the whole fermionic part of the Standard Model in this framework. Quarks and leptons fit naturally into the smallest typical and nontypical irreducible representations of the graded …

PhysicsNuclear and High Energy PhysicsParticle physicsHigh Energy Physics::PhenomenologyGraded ringAstronomy and AstrophysicsLie superalgebraNoncommutative geometryAtomic and Molecular Physics and OpticsSuper-Poincaré algebraGraded Lie algebraFiltered algebraTheoretical physicsLie algebraAlgebra representationInternational Journal of Modern Physics A
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Classical anomalies of supersymmetric extended objects

1991

Abstract The hamiltonian form of the action for a p-extended supersymmetric object is presented, and used to deduce both the algebra generated by the constraints, in agreement with previous results for p=1,2, and the algebra of the supersymmetry charges. The “anomalous” contributions in each algebra (for given p) are shown to be related, and the origin of their different properties is exhibited. In particular, it is shown why only in the charge algebra are the “anomalous” contributions always topological and the commutators of the translations always zero.

PhysicsSymmetric algebraNuclear and High Energy PhysicsConstraint algebraCurrent algebraSupersymmetrySuper-Poincaré algebraTheoretical physicssymbols.namesakeQuantum mechanicssymbolsAlgebra representationComposition algebraHamiltonian (quantum mechanics)Physics Letters B
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