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Lie algebras graded by finite root systems and the intersection matrix algebras of Slodowy. (English) Zbl 0778.17018
This paper concerns toroidal Lie algebras, certain intersection matrix Lie algebras defined by Slodowy, and their relationship to one another and to certain Lie algebra analogues of Steinberg groups. The main result of the paper is the identification of the intersection matrix algebras arising from multiply-affinized Cartan matrices of types $$A$$, $$D$$ and $$E$$ with certain Steinberg Lie algebras and toroidal Lie algebras. A major part of the paper studies and classifies Lie algebras graded by finite root systems. These become the principal tool in the analysis of intersection matrix algebras.

##### MSC:
 17B65 Infinite-dimensional Lie (super)algebras 17B70 Graded Lie (super)algebras
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##### References:
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