A note on homomorphisms of matrix semigroup - Omladič, Matjaž (Ars mathematica contemporanea, 2013)
Let ?$\mathbb{F}$? be a field. We classify multiplicative maps from ?${\mathcal M}_n(\mathbb{F})$? to ?${\mathcal M}_{n \choose k}(\mathbb{F})$? which annihilate a zero matrix and map rank-?$k$? matrix into a rank-one matrix.
Keywords: homomorphism; matrix semigroup; representation