HNN extensions with lower bounded inverse monoids

On the structure of lower bounded HNN extensions

“…1. We review some definitions and results from [5]. We consider an HNN extension S * = [S; U 1 , U 2 ; φ] of an inverse semigroup S where U 1 and U 2 are inverse monoids that are lower bounded in S, with respective identities e 1 and e 2 , and φ : U 1 → U 2 is an isomorphism.…”

“…Construction 3.1. [5,Construction 3.5] Let A be a t-cactoid inverse automaton over X ∪ {t} that is closed, relative to X ∪ {t} | R . Suppose v 1 → t v 2 is a t-edge of A and we have a loop v 1 → f v 1 in (v 1 ), for some f ∈ E(U 1 ), and no loop v 2 → (f )φ v 2 in (v 2 ).…”

“…The theory of lower bounded HNN extensions has been generalized by the authors in [5]. An inverse subsemigroup is called lower bounded in if, for any and with in , there exists with in .…”

“…1. We review some definitions and results from [5].

Figure 1. The lower bounded subsemigroup condition.

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“…Lemma 3.31] If is a t-opuntoid graph with finitely many S -lobes, then the automorphism group of is embedded into the automorphism group of some S -lobe of . Lemma 3.11 [5,. Lemma 3.32] Let be a complete t-opuntoid graph that has a host.…”