Singular quadratic Lie superalgebras
Type de document :
Compte-rendu et recension critique d'ouvrage
Titre :
Singular quadratic Lie superalgebras
Auteur(s) :
Duong, Minh Thanh [Auteur]
Ushirobira, Rosane [Auteur]
Non-Asymptotic estimation for online systems [NON-A]
Institut de Mathématiques de Bourgogne [Dijon] [IMB]
Ushirobira, Rosane [Auteur]
Non-Asymptotic estimation for online systems [NON-A]
Institut de Mathématiques de Bourgogne [Dijon] [IMB]
Titre de la revue :
Journal of Algebra
Pagination :
372 - 412
Éditeur :
Elsevier
Date de publication :
2014
ISSN :
0021-8693
Mot(s)-clé(s) en anglais :
17B30
17B05
Adjoint orbits 2000 MSC: 15A63
Invariant
17B70
Double extensions
Super Poisson bracket
Quadratic Lie superalgebras
Generalized double extensions
17B05
Adjoint orbits 2000 MSC: 15A63
Invariant
17B70
Double extensions
Super Poisson bracket
Quadratic Lie superalgebras
Generalized double extensions
Discipline(s) HAL :
Mathématiques [math]/Théorie des représentations [math.RT]
Résumé en anglais : [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 ...
Lire la suite >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.Lire moins >
Lire la suite >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.Lire moins >
Langue :
Anglais
Vulgarisation :
Non
Collections :
Source :
Fichiers
- https://hal.inria.fr/hal-01114188/document
- Accès libre
- Accéder au document
- http://arxiv.org/pdf/1206.5504
- Accès libre
- Accéder au document
- https://hal.inria.fr/hal-01114188/document
- Accès libre
- Accéder au document
- https://hal.inria.fr/hal-01114188/document
- Accès libre
- Accéder au document
- https://hal.inria.fr/hal-01114188/document
- Accès libre
- Accéder au document
- document
- Accès libre
- Accéder au document
- DU-super.pdf
- Accès libre
- Accéder au document
- 1206.5504
- Accès libre
- Accéder au document