Showing papers on "Cartan matrix published in 1971"

Lie algebras and locally compact groups

Abstract: This volume presents lecture notes based on the author's courses on Lie algebras and the solution of Hilbert's fifth problem. In chapter 1, "Lie Algebras," the structure theory of semi-simple Lie algebras in characteristic zero is presented, following the ideas of Killing and Cartan. Chapter 2, "The Structure of Locally Compact Groups," deals with the solution of Hilbert's fifth problem given by Gleason, Montgomery, and Zipplin in 1952.

Irreducible Lie algebras of infinite type

Abstract: Let F be a finite dimensional vector space over an algebraically closed field of characteristic^2, 3, 5. It is shown that if LCZg\(V) is an irreducible Lie algebra of infinite type then either L=gl(F), L=s\(V), dim F = 2r^4 and L=sp(F), dim V = 2r^4 and L =csp(F), or there exists A E.L such that ad A 5^0 = (ad A)2. As a corollary we obtain E. Cartan's classification of the irreducible Lie algebras of infinite type over C. Let L be a Lie algebra of linear transformations of a vector space V. For each nonnegative integer n the nth Cartan prolongation, Ln, is defined inductively by La = L and

Theorems on Cartan subalgebras like some on Carter subgroups

Abstract: We consider some results on the Cartan subalgebras of a solvable Lie algebra which are analogues to some results on Carter subgroups of a finite solvable group. Only solvable Lie algebras are considered here.