Socle and some invariants of quadratic Lie superalgebras

DOI10.1016/S0021-8693(02)00682-8zbMath1013.17029WikidataQ115340510 ScholiaQ115340510MaRDI QIDQ1870084

Saïd Benayadi

Publication date: 4 May 2003

Published in: Journal of Algebra (Search for Journal in Brave)

zbMATH Keywords

invariantssimple Lie superalgebrassocleconverse of Koszul's theoremminimal graded ideals

Mathematics Subject Classification ID

Graded Lie (super)algebras (17B70)

Related Items (22)

Tools to specify semi-simple Jordan triple systems ⋮ Quadratic Malcev Superalgebras with Reductive Even Part ⋮ Nondegenerate invariant symmetric bilinear forms on simple Lie superalgebras in characteristic 2 ⋮ Invariant bilinear forms on Leibniz superalgebras ⋮ Lie algebras with quadratic dimension equal to 2 ⋮ Hom-Lie algebras with symmetric invariant nondegenerate bilinear forms ⋮ Symplectic double extensions for restricted quasi-Frobenius Lie (super)algebras ⋮ Singular quadratic Lie superalgebras ⋮ Double extensions of restricted Lie (super)algebras ⋮ Poisson algebras and symmetric Leibniz bialgebra structures on oscillator Lie algebras ⋮ The Socle of a Metricn-Lie Algebra ⋮ Quadratic Color Hom-Lie Algebras ⋮ LIE SUPERALGEBRAS WITH SOME HOMOGENEOUS STRUCTURES ⋮ A new invariant of quadratic Lie algebras ⋮ Leibniz Algebras with Invariant Bilinear Forms and Related Lie Algebras ⋮ Odd-quadratic Lie superalgebras ⋮ Double extensions of Lie superalgebras in characteristic 2 with nondegenerate invariant supersymmetric bilinear form ⋮ Quadratic Lie superalgebras with a reductive even part ⋮ Quadratic symplectic Lie superalgebras and Lie bi-superalgebras ⋮ Symmetric Novikov superalgebras ⋮ Quadratic (resp. symmetric) Leibniz superalgebras ⋮ Leibniz central extensions of Lie superalgebras

Cites Work

• The theory of Lie superalgebras. An introduction
• Quadratic Lie superalgebras with the completely reducible action of the even part of the odd part
• The root space decompositions of the quadratic Lie superalgebras
• QUADRATIC LIE ALGEBRAS AND COMMUTATIVE ASSOCIATIVE ALGEBRAS
• Algèbres de Lie et produit scalaire invariant
• Double extension of quadratic lie superalgebras
• A new characterization of semisimple Lie algebras
• Lie algebras admitting a unique quadratic structure
• Cohomology of Lie superalgebras and their generalizations
• Outer Derivations of Lie Algebras
• Homologie et cohomologie des algèbres de Lie
• Lie superalgebras
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