Semigroups of the basic affine lie group and their automorphisms

Abstract

UDC 519.46 In recent years the theory of semigroups of Lie groups has been intensively studied. The problem of calculating the automorphisms of connected subsemigroups generates particular interest. For Abelian Lie groups this problem has been completely solved by A.D. Aleksandrov [1]. However, for noncom- mutative Lie groups, no notable results have been obtained yet (the basic affine Lie group [2, 3] and 3-dimensional Lie groups [4] being exceptions). In this article we find the automorphisms of connected subsemigroups with quasicontingency of the form L x K (see Definition 1 below) for the case of the basic anne Lie group. This completely solves the problem of computing the automorphisms of subsemigroups of the basic affine Lie group. The basic anne Lie group is a connected simply connected real Lie group whose Lie algebra is given, in a suitable basis X1,..., Xn, by nontrivial commutation relations