Abstract:
We use standard notations of [FH, S]; for a precise definition of the Cartan prolongation and its generalizations (Cartan-Tanaka-Shchepochkina or CTS- prolongations), see [Shch]; see also [BGL3]{[BGL5], [Leb1, Leb2]. Hereafter K is an algebraically closed (unless finite) field, charK = p. The works of S. Lie, Killing and Cartan, now classical, completed classifi- cation over C of simple Lie algebras of finite dimension and certain infinite dimensional (of polynomial vector fields, or \vectorial" Lie algebras). In addition to the above two types, there are several more interesting types of simple Lie algebras but they do not contribute to the solution of our problem: classification of simple finite dimensional modular Lie (su- per)algebras, except one: the queer type described below (and, perhaps, examples, for p = 2, of the types described in [J, Sh] and their generalizations, if any). Observe that all finite dimensional simple Lie algebras are of the form g(A); for their definition embracing the modular case and the classification, see [BGL5]. Lie algebras and Lie superalgebras over fields in characteristic p > 0, a.k.a. modular Lie (super)algebras, were distinguished in topology in the 1930s. The simple Lie algebras drew attention (over fnite fields K) as a byproduct of classification of simple finite groups, cf. [St]. Lie superalgebras, even simple ones, did not draw much attention of mathematicians until their (outstanding) usefulness was observed by physicists in the 1970s. Researchers discovered more and more of new examples of simple modular Lie algebras for decades
Page(s):
101-110
DOI:
DOI not available
Published:
Journal: Journal of Prime Research in Mathematics, Volume: 3, Issue: 0, Year: 2007