Algebraic Geometry Seminar
Wednesday, February 18, 2004, 4:00pm, 120 Physics
Hayk Melikyan (North Carolina Central University)
Modular simple Lie algebras

Abstract:

In this talk we will give a comprehensive overview of all known finite dimensional simple Lie algebras in characteristic p > 3 and discuss some aspects of classification problem for small characteristics 2 and 3. The problem of classifying the finite-dimensional simple Lie algebras of characteristic p > 0 is a long-standing one. Work on this question during the last forty years has been directed by the Kostrikin-Shafarevich Conjecture, which states: Over an algebraically closed field of characteristic p > 5 a finite-dimensional restricted simple Lie algebra is classical or of Cartan type. All known finite dimensional simple Lie algebras over an algebraically closed field of characteristic p > 5 split into two families. The classical Lie algebras, the analogues of the finite-dimensional simple complex Lie algebras (closely related to the Lie algebras of simple algebraic groups), and the finite dimensional graded Cartan type Lie algebras (analogs of infinite-dimensional complex Lie algebras of Cartan) and their filtered deformations Recently A. Premet and H. Strade announced the classification of simple Lie algebras over a field of characteristic p >3. All finite dimensional simple Lie algebras over an algebraically closed field K of characteristic p > 3 split into three families: classical Lie algebras, Cartan type Lie algebras, and the Melikyan algebras.

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