Maximal Inverse Subsemigroups of the Symmetric Inverse Semigroup on a Finite-Dimensional Vector Space

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).