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- Title
ON A NEW APPROACH TO THE DUAL SYMMETRIC INVERSE MONOID $\mathcal{I}_{X}^{\ast}$.
- Authors
MALTCEV, VICTOR
- Abstract
We construct the inverse partition semigroup$\mathcal{IP}_{X}$, isomorphic to the dual symmetric inverse monoid$\mathcal{I}_{X}^{\ast}$, introduced in [6]. We give a convenient geometric illustration for elements of $\mathcal{IP}_{X}$. We describe all maximal subsemigroups of $\mathcal{IP}_{X}$ and find a generating set for $\mathcal{IP}_{X}$ when X is finite. We prove that all the automorphisms of $\mathcal{IP}_{X}$ are inner. We show how to embed the symmetric inverse semigroup into the inverse partition one. For finite sets X, we establish that, up to equivalence, there is a unique faithful effective transitive representation of $\mathcal{IP}_{n}$, namely to $\mathcal{IS}_{2^{n}-2}$. Finally, we construct an interesting $\mathcal{H}$-cross-section of $\mathcal{IP}_{n}$, which is reminiscent of $\mathcal{IO}_{n}$, the $\mathcal{H}$-cross-section of $\mathcal{IS}_{n}$, constructed in [4].
- Subjects
MONOIDS; SEMIGROUPS (Algebra); AUTOMORPHISMS; GROUP theory; MATHEMATICAL symmetry
- Publication
International Journal of Algebra & Computation, 2007, Vol 17, Issue 3, p567
- ISSN
0218-1967
- Publication type
Article
- DOI
10.1142/S0218196707003792