LAUSR

In 2016, Alm–Hirsch–Maddux defined relation algebras $$\mathfrak {L}(q,n)$$L(q,n) that generalize Roger Lyndon’s relation algebras from projective lines, so that $$\mathfrak {L}(q,0)$$L(q,0) is a Lyndon algebra. In that paper, it was shown that if $$q>2304n^2+1$$q>2304n2+1, then $$\mathfrak {L}(q,n)$$L(q,n) is representable, and if $$q<2n$$q<2n, then $$\mathfrak {L}(q,n)$$L(q,n) is not representable. In the present paper, we reduced this gap by proving that if $$q\ge n(\log n)^{1+\varepsilon }$$q≥n(logn)1+ε, then $$\mathfrak {L}(q,n)$$L(q,n) is representable.