On rigid Hermitean lattices, II
We study the indexed Hermitean lattice of type 0 generated by a single element a subjected to the relation a ≤ b⊥ ∧ bb⊥= 0. We prove that it is finite, provided that two crucial indices are finite. We show that index relations imply algebraic relations and describe the lattice by means of its subdirectly irreducible factors. We finally use the results to confirm a conjecture appeared in 2000.
[DM2] A.C. de la Maza, R.Moresi, Hermitean (semi) lattices and Rolf ’s lattice, Algebra Universalis 66 (2011), 49-62.
[DM3] A.C. de la Maza, R.Moresi, On rigid Hermitean lattices, I, Preprint.
[G1] H. Gross, Quadratic forms in infinite dimensional vector spaces, Birk¨
[KKW] H. A. Keller, U.-M. K¨unzi, M. Wild (eds), Orthogonal geometry in infinite dimensional vector spaces, Heft 53, Bayreuther Mathematische Schriften, Bayreuth, 1998.
[M1] R. Moresi, Modular lattices and Hermitean forms, Algebra Universalis 22 (1986), 279-297.
[M2] R. Moresi, A test-example of a quadratic lattice, Order 17 (2000), 215-226.
[R] H. L. Rolf, The free lattice generated by a set of chains, Pacific J. Math. 8 (1958), 585-595.
[S] E. T. Schmidt, On finitely generated simple modular lattice, Periodica Mathematica Hungarica 6(3) (1975), 213-216.