Graded contractions of bilinear invariant forms of Lie algebras

Abstract

We introduce a new construction of bilinear invariant forms on Lie algebras, based on the method of graded contractions. The general method is described and the ${\mathbb{Z}}_2$-, ${\mathbb{Z}}_3$-, and ${\mathbb{Z}}_2\otimes {\mathbb{Z}}_2$-contractions are found. The results can be applied to all Lie algebras and superalgebras (finite or infinite dimensional) which admit the chosen gradings. We consider some examples: contractions of the Killing form, toroidal contractions of $su(3)$, and we briefly discuss the limit to new WZW actions.

15 pages

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Cited by in corpus (3)

• Casimir invariants for the complete family of quasi-simple orthogonal algebras
• Graded Contractions of Affine Kac-Moody Algebras
• Contractions from Grading