Algebra Seminar

Permutation-Hermite equivalence for integer matrices
Monday, 13 February 2017 - 1:10 pm to 1:40 pm
Room number: 
FSS 8003
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Free of charge
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SPEAKER: David Handelman (Ottawa) DATE: Monday, February 13, 2017 TIME: 1:10 pm ROOM: FSS 8003 ABSTRACT: Permutation-Hermite (PH) equivalence on integer matrices, or equivalently on subgroups of Zn, is an equivalence relation intermediate between the usual Smith equivalence (invertible row and column operations) and Hermite equivalence (invertible row operations)—invertible row operations as well as column permutations are allowed. It comes up in a few places, e.g., classification of lattice simplices up to the action AGL(n,Z), but for me, it arose from classification of dense subgroups of Rn that are free of rank n+1 (the minimum possible) as partially ordered abelian groups. <p>Relatively easily computed invariants for PH-equivalence are given that together are pretty good, and a notion of duality (previously observed in the lattice simplex situation) yields still more. This is a subject still in its naissance, so numerous examples and conjectures will be discussed.