Abstract
Let d > 0 be a square-free integer, and let Ld be the corresponding Hilbert lattice. Suppose given a finite-index subgroup Γ of O+(Ld) generated by reflections and containing -id and let A(Γ) be the algebra of Γ-automorphic forms. It is proved that if the algebra A(Γ) is free, then d ∈ {2, 3, 5, 6,13, 21}.
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