Search results for "Lie superalgebra"

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.

The graded Lie algebra structure of Lie superalgebra deformation theory

1989

We show how Lie superalgebra deformation theory can be treated by graded Lie algebras formalism. Rigidity and integrability theorems are obtained.

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

1990

International audience

Indecomposable modules over the Virasoro Lie algebra and a conjecture of V. Kac

1991

We consider a class of indecomposable modules over the Virasoro Lie algebra that we call bounded admissible modules. We get results concerning the center and the dimensions of the weight spaces. We prove that these modules always contain a submodule with one-dimensional weight spaces. From this follows the proof of a conjecture of V. Kac concerning the classification of simple admissible modules.

Jeu de taquin and diamond cone for Lie (super)algebras

2015

Abstract In this paper, we recall combinatorial basis for shape and reduced shape algebras of the Lie algebras gl ( n ) , sp ( 2 n ) and so ( 2 n + 1 ) . They are given by semistandard and quasistandard tableaux. Then we generalize these constructions to the case of the Lie superalgebra spo ( 2 n , 2 m + 1 ) . The main tool is an extension of Schutzenberger's jeu de taquin to these algebras.

Contractions yielding new supersymmetric extensions of the poincaré algebra

1991

Two new Poincare superalgebras are analysed. They are obtained by the Wigner-Inonu contraction from two real forms of the superalgebra OSp(2;4;C) - one describing the N = 2 anti-de-Sitter superalgebra with a non-compact internal symmetry SO(1, 1) and the other corresponding to the de-Sitter superalgebra with internal symmetry SO(2). Both are 19-dimensional self-conjugate extensions of the Konopel'chenko superalgebra. They contain 10 Poincare generators and one generator of internal symmetry in addition to 8 odd generators half of which, however, do not commute with translations.

On codimension growth of finite-dimensional Lie superalgebras

2012

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 …

Graded polynomial identities and Specht property of the Lie algebrasl2

2013

Abstract Let G be a group. The Lie algebra sl 2 of 2 × 2 traceless matrices over a field K can be endowed up to isomorphism, with three distinct non-trivial G-gradings induced by the groups Z 2 , Z 2 × Z 2 and Z . It has been recently shown (Koshlukov, 2008 [8] ) that for each grading the ideal of G-graded identities has a finite basis. In this paper we prove that when char ( K ) = 0 , the algebra sl 2 endowed with each of the above three gradings has an ideal of graded identities Id G ( sl 2 ) satisfying the Specht property, i.e., every ideal of graded identities containing Id G ( sl 2 ) is finitely based.

Nambu structures and super-theorem of Amitsur-Levitzki

2004

In this thesis, we establish new polynomial identities in a non commutative combinatorial framework. In the first part, we present new Nambu-Lie structures by classifying all (n-1)-structures in \R^n and we give a method for defining all-order brackets in Lie algebras. We are able to quantify one of our structures, thanks to standard polynomials and even Clifford algebras. In the second part of our work, we generalize the notion of standard polynomials to graded algebras, and we prove an Amitsur-Levitzki type theorem for the Lie superalgebras \osp(1,2n) inspired by Kostant's cohomological interpretation of the classical theorem. We give super versions of properties and results needed in Kos…