Simple Lie Algebras of Small Characteristic II. Exceptional Roots
โ Scribed by Alexander Premet; Helmut Strade
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 781 KB
- Volume
- 216
- Category
- Article
- ISSN
- 0021-8693
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โฆ Synopsis
Let L be a finite dimensional simple Lie algebra of absolute toral rank 2 over an algebraically closed field of characteristic p ) 3 and T a 2-dimensional torus in the semisimple p-envelope of L. Suppose that L is not isomorphic to a Melikian ลฝ . algebra. It is proved in this paper that, for every root โฃ g โซ L, T , the subalgebra
In particular, this implies that, in the terminology of R. E. Block ลฝ . ลฝ .
๐ SIMILAR VOLUMES
It is proved that every finite dimensional simple Lie algebra of absolute toral rank 2 over an algebraically closed field of characteristic p ) 3 is of classical or Cartan type or a Melikian algebra.
We construct here several classes of simple Lie algebras of characteristic ลฝ . 0 which include the Virasoro algebra without central charge and the graded Lie algebras of Cartan type. Our construction is motivated by our w x recent construction of simple locally Novikov algebras in 5 . Our simple Li
We present a combinatorial algorithm for computing the positive roots of all nine types of simple Lie algebras over complexes. It was implemented on a programmable desk calculator. Simple Lie algebras play a key role in many bran-6