The alternative torus and the structure of elliptic quasi-simple Lie algebras of type 𝐴₂

Berman, Stephen; Gao, Yun; Krylyuk, Yaroslav; Neher, Erhard

doi:10.1090/S0002-9947-1995-1303115-1

The alternative torus and the structure of elliptic quasi-simple Lie algebras of type $A_ 2$
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by Stephen Berman, Yun Gao, Yaroslav Krylyuk and Erhard Neher

Trans. Amer. Math. Soc. 347 (1995), 4315-4363

DOI: https://doi.org/10.1090/S0002-9947-1995-1303115-1

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Abstract:

We present the complete classification of the tame irreducible elliptic quasi-simple Lie algebras of type ${A_2}$, and in particular, specialize on the case where the coordinates are not associative. Here the coordinates are Cayley-Dickson algebras over Laurent polynomial rings in $\nu \geqslant 3$ variables, which we call alternative tori. In giving our classification we need to present much information on these alternative tori and the Lie algebras coordinatized by them.

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