On universal objects in the class of graph inverse semigroups

2017/08/30 by Bardyla, Serhii
#FOS: Mathematics #General Topology (math.GN) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1709.01393

Abstract

In this paper we show that polycyclic monoids are universal objects in the class of graph inverse semigroups. In particular, we prove that a graph inverse semigroup G(E) over a directed graph E embeds into the polycyclic monoid P_λ where λ=|G(E)|. We show that each graph inverse semigroup G(E) admits the coarsest inverse semigroup topology τ. Moreover, each injective homomorphism from (G(E),τ) to the (P_|G(E)|,τ) is a topological embedding.

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