How to realize Lie algebras by vector fields

Details How to realize Lie algebras by vector fields How to realize Lie algebras by vector fields

2005-09-21

arxiv.org/abs/math/0509472v1

Mathematics

Representation Theory

17 pages, LaTeX

Scientific paper

10.1007/s11232-006-0078-5

An algorithm for embedding finite dimensional Lie algebras into Lie algebras of vector fields (and Lie superalgebras into Lie superalgebras of vector fields) is offered in a way applicable over ground fields of any characteristic. The algorithm is illustrated by reproducing Cartan's interpretations of the Lie algebra of G(2) as the Lie algebra that preserves certain non-integrable distributions. Similar algorithm and interpretation are applicable to other exceptional simple Lie algebras, as well as to all non-exceptional simple ones and many non-simple ones, and to many Lie superalgebras.

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