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Prime L-algebras and right-angled Artin groups

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Abstract

Self-similar monoids arising from \(\wedge \)-semilattices with greatest element 1 are characterized by generators and relations and put into one-to-one correspondence with a class of right-angled Artin groups. The (not necessarily finitely generated) Artin groups arising in this way are shown to have a right invariant directed order and admit a non-commutative variant of unique prime factorization.

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  1. Institute for Algebra and Number Theory, University of Stuttgart, Pfaffenwaldring 57, 70550, Stuttgart, Germany

    Wolfgang Rump

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  1. Wolfgang Rump
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Correspondence to Wolfgang Rump.

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Communicated by Mark V. Lawson.

Dedicated to B. V. M.

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Rump, W. Prime L-algebras and right-angled Artin groups. Semigroup Forum 106, 481–503 (2023). https://doi.org/10.1007/s00233-023-10343-4

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