Affinely spanned quasi-stochastic algebraic monoids

摘要

A linear algebraic monoid over an algebraically closed field K of characteristic zero is called (row) quasi-stochastic if each row of each matrix element is of sum one. Any linear algebraic monoid over K can be embedded as an algebraic submonoid of the maximum affinely spanned quasi-stochastic monoid of some degree n. The affinely spanned quasistochastic algebraic monoids form a basic class of quasi-stochastic algebraic monoids. An initial study of structure of affinely spanned quasi-stochastic algebraic monoids is conducted. Among other things, it is proved that the Zariski closure of a parabolic subgroup of the unit group of an affinely spanned quasi-stochastic algebraic monoid is affinely spanned.