Products of conjugacy classes in algebraic groups. I (Q1891765)

This paper is the first in a series of 2 papers. It begins with conjugacy classes in algebraic groups and considers algebraic varieties which can be presented as closures of products of such conjugacy classes. It includes estimates on the dimension of such varieties and applies it to invariant theory. In the second part, the author treats \(SL_n (K)\) and describes the structure of the monoid generated by its semisimple conjugacy classes. [For part II of this paper see ibid. 745-779 (1995; see the following review)].