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Transactions of the American Mathematical Society

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The alternative torus and the structure of elliptic quasi-simple Lie algebras of type $ A\sb 2$


Authors: Stephen Berman, Yun Gao, Yaroslav Krylyuk and Erhard Neher
Journal: Trans. Amer. Math. Soc. 347 (1995), 4315-4363
MSC: Primary 17B37; Secondary 17B67
DOI: https://doi.org/10.1090/S0002-9947-1995-1303115-1
MathSciNet review: 1303115
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1995-1303115-1
Article copyright: © Copyright 1995 American Mathematical Society

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