Representability of Lyndon-Maddux relation algebras

Jeremy F. Alm

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arXiv · 1703.06314

Representability of Lyndon-Maddux relation algebras

Jeremy F. Alm

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Abstract

In Alm-Hirsch-Maddux (2016), relation algebras $\mathfrak{L}(q,n)$ were defined that generalize Roger Lyndon's relation algebras from projective lines, so that $\mathfrak{L}(q,0)$ is a Lyndon algebra. In that paper, it was shown that if $q>2304n^2+1$, $\mathfrak{L}(q,n)$ is representable, and if $q<2n$, $\mathfrak{L}(q,n)$ is not representable. In the present paper, we reduced this gap by proving that if $q\geq n(\log n)^{1+\varepsilon}$, $\mathfrak{L}(q,n)$ is representable.

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Jeremy F. Alm. 2017-03-18. Representability of Lyndon-Maddux relation algebras. https://arxiv.org/abs/1703.06314

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