Title :

Singular quadratic Lie superalgebras

Author(s) :

Duong, Minh Thanh [Auteur]
Ushirobira, Rosane [Auteur]
Institut de Mathématiques de Bourgogne [Dijon] [IMB]
Non-Asymptotic estimation for online systems [NON-A]

Journal title :

Journal of Algebra

Pages :

372 - 412

Publisher :

Elsevier

Publication date :

2014

ISSN :

0021-8693

English keyword(s) :

17B30
17B05
Adjoint orbits 2000 MSC: 15A63
Invariant
17B70
Double extensions
Super Poisson bracket
Quadratic Lie superalgebras
Generalized double extensions

HAL domain(s) :

Mathématiques [math]/Théorie des représentations [math.RT]

English abstract : [en]

In this paper, we generalize some results on quadratic Lie algebras to quadratic Lie superalgebras, by applying graded Lie algebras tools. We establish a one-to-one correspondence between non-Abelian quadratic Lie superalgebra ...
Show more >In this paper, we generalize some results on quadratic Lie algebras to quadratic Lie superalgebras, by applying graded Lie algebras tools. We establish a one-to-one correspondence between non-Abelian quadratic Lie superalgebra structures and nonzero even super-antisymmetric 3-forms satisfying a structure equation. An invariant number of quadratic Lie superalgebras is then defined, called the dup-number. Singular quadratic Lie superalgebras (i.e. those with nonzero dup-number) are studied. We show that their classification follows the classifications of O(m)-adjoint orbits of o(m) and Sp(2n)-adjoint orbits of sp(2n). An explicit formula for the quadratic dimension of singular quadratic Lie superalgebras is also provided. Finally, we discuss a class of 2-nilpotent quadratic Lie superalgebras associated to a particular super-antisymmetric 3-form.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

Collections :

• Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189

Source :

Harvested from HAL