Showing papers on "Cartan matrix published in 1974"
TL;DR: In this paper, the irreducible representations of infinite-dimensional filtered Lie algebras are studied and the concept of the height of a representation is introduced, and it is proved that the representations of height greater than one of the Lie algesbras Wn, Sn, Hn and Kn are induced.
Abstract: In this paper the irreducible representations of infinite-dimensional filtered Lie algebras are studied. The concept of the height of a representation is introduced, and it is proved that the representations of height greater than one of the Lie algebras Wn, Sn, Hn and Kn are induced. The representations of height one of the algebras Wn are also described.
108 citations
TL;DR: In this article, the classification of finite-dimensional filtered Lie algebras over fields of prime characteristic whose associated graded Lie algesbras are Cartan type is studied, and a description of infinite-dimensional primitive transitive subalgebra of linear differential operators with coefficients in a subring of the ring of formal power series is given.
Abstract: The main results of this article are: 1) the classification of those finite-dimensional filtered Lie algebras over fields of prime characteristic whose associated graded Lie algebras are Lie algebras of Cartan type; 2) a description of the infinite-dimensional primitive transitive subalgebras of Lie algebras of linear differential operators with coefficients in a subring of the ring of formal power series over a field of characteristic zero.
105 citations