### Abstract

A Lie (super)algebra with a non-degenerate invariant symmetric bilinear form will be called a NIS-Lie (super)algebra. The double extension of a NIS-Lie (super)algebra is the result of simultaneously adding to it a central element and an outer derivation so that the larger algebra has also a NIS. Affine loop algebras, Lie (super)algebras with symmetrizable Cartan matrix over any field, Manin triples, symplectic reflection (super)algebras are among the Lie (super)algebras suitable to be doubly extended. We consider double extensions of Lie superalgebras in characteristic 2, and concentrate on peculiarities of these notions related with the possibility for the bilinear form, the center, and the derivation to be odd. Two Lie superalgebras we discovered by this method are indigenous to the characteristic 2.

Original language | English (US) |
---|---|

Pages (from-to) | 141-179 |

Number of pages | 39 |

Journal | Journal of Algebra |

Volume | 510 |

DOIs | |

State | Published - Sep 15 2018 |

### Fingerprint

### Keywords

- Characteristic 2
- Double extension
- Lie superalgebra

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Journal of Algebra*,

*510*, 141-179. https://doi.org/10.1016/j.jalgebra.2018.06.005

**Double extensions of Lie superalgebras in characteristic 2 with nondegenerate invariant supersymmetric bilinear form.** / Benayadi, Saïd; Bouarroudj, Sofiane.

Research output: Contribution to journal › Article

*Journal of Algebra*, vol. 510, pp. 141-179. https://doi.org/10.1016/j.jalgebra.2018.06.005

}

TY - JOUR

T1 - Double extensions of Lie superalgebras in characteristic 2 with nondegenerate invariant supersymmetric bilinear form

AU - Benayadi, Saïd

AU - Bouarroudj, Sofiane

PY - 2018/9/15

Y1 - 2018/9/15

N2 - A Lie (super)algebra with a non-degenerate invariant symmetric bilinear form will be called a NIS-Lie (super)algebra. The double extension of a NIS-Lie (super)algebra is the result of simultaneously adding to it a central element and an outer derivation so that the larger algebra has also a NIS. Affine loop algebras, Lie (super)algebras with symmetrizable Cartan matrix over any field, Manin triples, symplectic reflection (super)algebras are among the Lie (super)algebras suitable to be doubly extended. We consider double extensions of Lie superalgebras in characteristic 2, and concentrate on peculiarities of these notions related with the possibility for the bilinear form, the center, and the derivation to be odd. Two Lie superalgebras we discovered by this method are indigenous to the characteristic 2.

AB - A Lie (super)algebra with a non-degenerate invariant symmetric bilinear form will be called a NIS-Lie (super)algebra. The double extension of a NIS-Lie (super)algebra is the result of simultaneously adding to it a central element and an outer derivation so that the larger algebra has also a NIS. Affine loop algebras, Lie (super)algebras with symmetrizable Cartan matrix over any field, Manin triples, symplectic reflection (super)algebras are among the Lie (super)algebras suitable to be doubly extended. We consider double extensions of Lie superalgebras in characteristic 2, and concentrate on peculiarities of these notions related with the possibility for the bilinear form, the center, and the derivation to be odd. Two Lie superalgebras we discovered by this method are indigenous to the characteristic 2.

KW - Characteristic 2

KW - Double extension

KW - Lie superalgebra

UR - http://www.scopus.com/inward/record.url?scp=85048711140&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85048711140&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2018.06.005

DO - 10.1016/j.jalgebra.2018.06.005

M3 - Article

VL - 510

SP - 141

EP - 179

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -