Quasiclassical Lie algebras

In this paper we study finite dimensional non-semisimple Lie algebras that can be obtained as Lie algebras of skew-symmetric elements of associative a lgebras with involution. We call such algebras quasiclassical and character ize them in terms of existence of so-called "*-plain" representations.We sh ow that the theory of *-plain representations for quasiclassical Lie algebr as is almost equivalent to representation theory of associative algebras wi th involution. (C) 2001 Academic Press.