On the subsemigroup complex of an aperiodic Brandt semigroup

Speaker
(Prof. Pedro Silva (CMUP, University of Porto
Date
22/10/2017 - 13:00 - 12:00Add to Calendar 2017-10-22 12:00:00 2017-10-22 13:00:00 On the subsemigroup complex of an aperiodic Brandt semigroup Taking as departure point an article by Cameron, Gadouleau, Mitchell and Peresse on maximal lengths of subsemigroup chains, we introduce the subsemigroup complex H(S) of a nite semigroup S as a (boolean representable) simplicial complex de fined through chains in the lattice of subsemi- groups of S. The rank of H(S) is the above maximal length minus one and H(S) provides other useful invariants concerning the lattice of subsemigroups of S. We present a research program for such complexes, illustrated through the particular case of combinatorial Brandt semigroups. The results include alternative characterizations of independence and bases, asymptotical estimates on the number of bases, or establishing when the complex is pure or a matroid. This is joint work with Stuart Margolis (Bar-Ilan University, Ramat Gan, Israel) and John Rhodes (University of California, Berkeley, USA). Building 216, Room 201 אוניברסיטת בר-אילן - Department of Mathematics mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
Building 216, Room 201
Abstract

Taking as departure point an article by Cameron, Gadouleau, Mitchell and Peresse on maximal
lengths of subsemigroup chains, we introduce the subsemigroup complex H(S) of a
nite semigroup
S as a (boolean representable) simplicial complex de
fined through chains in the lattice of subsemi-
groups of S. The rank of H(S) is the above maximal length minus one and H(S) provides other
useful invariants concerning the lattice of subsemigroups of S. We present a research program for
such complexes, illustrated through the particular case of combinatorial Brandt semigroups. The
results include alternative characterizations of independence and bases, asymptotical estimates on
the number of bases, or establishing when the complex is pure or a matroid.

This is joint work with Stuart Margolis (Bar-Ilan University, Ramat Gan, Israel) and John
Rhodes (University of California, Berkeley, USA).

Last Updated Date : 19/10/2017