Embedding Finite Involution Semigroups in Matrices with Transposition
Discrete Applied Mathematics
Semigroup, Involution semigroup, Inverse semigroup, Semigroup of matrices, Transposition, Embedding
The present article establishes two contrasting results: a finite involution semigroup is embeddable in some semigroup of complex matrices with conjugate transposition if and only if it is an inverse semigroup, while every finite involution semigroup is embeddable in some semigroup of binary matrices with the skew transposition across the secondary diagonal.
Lee, Edmond W. H., "Embedding Finite Involution Semigroups in Matrices with Transposition" (2023). Mathematics Faculty Articles. 358.