Displaying similar documents to “Characteristic vectors of unimodular lattices which represent two”

Orthomodular Lattices

Elżbieta Mądra, Adam Grabowski (2008)

Formalized Mathematics

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The main result of the article is the solution to the problem of short axiomatizations of orthomodular ortholattices. Based on EQP/Otter results [10], we gave a set of three equations which is equivalent to the classical, much longer equational basis of such a class. Also the basic example of the lattice which is not orthomodular, i.e. benzene (or B6) is defined in two settings - as a relational structure (poset) and as a lattice.As a preliminary work, we present the proofs of the dependence...

S-extremal strongly modular lattices

Gabriele Nebe, Kristina Schindelar (2007)

Journal de Théorie des Nombres de Bordeaux

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S-extremal strongly modular lattices maximize the minimum of the lattice and its shadow simultaneously. They are a direct generalization of the s-extremal unimodular lattices defined in [6]. If the minimum of the lattice is even, then the dimension of an s-extremal lattices can be bounded by the theory of modular forms. This shows that such lattices are also extremal and that there are only finitely many s-extremal strongly modular lattices of even minimum.

Another 80-dimensional extremal lattice

Mark Watkins (2012)

Journal de Théorie des Nombres de Bordeaux

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We show that the unimodular lattice associated to the rank 20 quaternionic matrix group SL 2 ( F 41 ) ⊗ S ˜ 3 ⊂ GL 80 ( Z ) is a fourth example of an 80-dimensional extremal lattice. Our method is to use the positivity of the Θ -series in conjunction with an enumeration of all the norm 10 vectors. The use of Aschbacher’s theorem on subgroups of finite classical groups (reliant on the classification of finite simple groups) provides one proof that this lattice is distinct from the previous three, while computing the inner...

On the variety Csub ( D )

Václav Slavík (1991)

Commentationes Mathematicae Universitatis Carolinae

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The variety of lattices generated by lattices of all convex sublattices of distributive lattices is investigated.