Abstract
In this paper we study finite dimensional non-semisimple Lie algebras that can be obtained as Lie algebras of skew-symmetric elements of associative algebras with involution. We call such algebras quasiclassical and characterize them in terms of existence of so-called “∗-plain” representations. We show that the theory of ∗-plain representations for quasiclassical Lie algebras is almost equivalent to representation theory of associative algebras with involution.
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