Maximal inverse subsemigroups of the symmetric inverse semigroup on a finite-dimensional vector space

Abstract

Yang (1999) classified the maximal inverse subsemigroups of all the ideals of the symmetric inverse semigroup $I(X)$ defined on a finite set $X$. Here we do the same for the semigroup $I(V)$ of all one-to-one partial linear transformations of a finite-dimensional vector space. We also show that $I(X)$ is almost never isomorphic to $I(V)$ for any set $X$ and any vector space $V$, and prove that any inverse semigroup can be embedded in some $I(V)$.