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Helmut Strade

Publications and source records attributed to Helmut Strade.

4 recordsLinked to original sources
arXiv2008

Simple Lie algebras of small characteristic VI. Completion of the classification

Let L be a finite-dimensional simple Lie algebra over an algebraically closed field of F characteristic p>3. We prove that if the p-envelope of L in the derivation algebra of L contains nonstandard tori of maximal dimension, then p=5 and L is isomorphic to one of the Melikian algebras. Together with our earlier results this implies that any finite-dimensional simple Lie algebra over F is of classical, Cartan or Melikian type.

math.RT↗
arXiv2006

Classification of finite dimensional simple Lie algebras in prime characteristics

We give a comprehensive survey of the theory of finite dimensional Lie algebras over an algebraically closed field of characteristic p>0 and announce that for p>3 the classification of finite dimensional simple Lie algebras is complete. Any such Lie algebra is up to isomorphism either classical (i.e. comes from characteristic 0) or a filtered Lie algebra of Cartan type or a Melikian algebra of characteristic 5.

math.RA↗
arXiv2006

Simple Lie algebras of small characteristic V. The non-Melikian case

Let L be a finite dimensional simple Lie algebra over an algebraically closed field of characteristic p>3. We prove in this paper that if all tori of maximal dimansion in the semisimple p-envelope of L are standard, the L is up to isomorphism either a Lie algebra of type A_n, B_n, C_n, D_n, E_6, E_7, E_8, F_4, G_2 or a filtered Lie algebra of Cartan type. When p>5, the assumption on tori is fulfilled automatically and our result can be restated as follows: every finite dimensional simple Lie algebra over an algebraically closee field of characteristic p>5 is either classical or of Cartan type. This theorem settles the last remaining case p=7 of the Kostrikin-Shafarevich conjecture (from 1966).

math.RA↗