Graded contractions of bilinear invariant forms of Lie algebras

Details Graded contractions of bilinear invariant forms of Lie algebras Graded contractions of bilinear invariant forms of Lie algebras

1994-02-23

arxiv.org/abs/hep-th/9402132v2

J.Phys. A27 (1994) 4537-4548

Physics

High Energy Physics

High Energy Physics - Theory

15 pages

Scientific paper

10.1088/0305-4470/27/13/027

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 $\Bbb Z_2$-, $\Bbb Z_3$-, and $\Bbb Z_2\otimes\Bbb Z_2$-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.

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