Some strictly infinitesimally generated semigroups
A subsemigroup \(S\) of a Lie group \(G\) is said to be strictly infinitesimally generated if it is generated (as a semigroup) by a family of one-parameter semigroups. In this paper the author reviews the elementary Lie theory of such semigroups and establishes by direct computation that several classes of semigroups are infinitesimally generated including the expansion semigroup and contraction semigroup of Euclidean \(n\)-space, the semigroup of upper (or lower) triangular stochastic matrices and certain semigroups of totally positive matrices. In each case the author also computes the tangent wedge (in the Lie algebra) of these semigroups.
scientific article; zbMATH DE number 1283839