Abstract
This chapter focuses on certain equations in the algebra of a semi-simple infinitesimal group. The chapter presents the equations expressed in terms of linear operators d1…dr, satisfying the conditions dλ dμ - dμ dλ = Cσλμdσλμ, where Cσλμ are the constants of structure of a semi-simple group g. The general equations are formulated in terms of a tensor calculus or tensor algebra. The chapter describes how these equations can be taken as a method of approach to Cartan's topological theory of group-spaces, and of related spaces.
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