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On integral quadratic forms having commensurable groups of automorphisms



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Montesinos Amilibia, José María (2013) On integral quadratic forms having commensurable groups of automorphisms. Hiroshima mathematical journal, 43 (3). pp. 371-441. ISSN 0018-2079

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Official URL: http://projecteuclid.org/euclid.hmj/1389102581


We introduce two notions of equivalence for rational quadratic forms. Two n-ary rational quadratic forms are commensurable if they possess commensurable groups of automorphisms up to isometry. Two n-ary rational quadratic forms F and G are projectivelly equivalent if there are nonzero rational numbers r and s such that rF and sG are rationally equivalent. It is shown that if F\ and G\ have Sylvester signature {−,+,+,...,+} then F\ and G\ are commensurable if and only if they are projectivelly equivalent. The main objective of this paper is to obtain a complete system of (computable) numerical invariants of rational n-ary quadratic forms up to projective equivalence. These invariants are a variation of Conway's p-excesses. Here the cases n odd and n even are surprisingly different. The paper ends with some examples

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Addendum to ‘‘On integral quadratic forms having commensurable groups of automorphisms’’, disponible en http://projecteuclid.org/euclid.hmj/1419619751

Uncontrolled Keywords:11E04: Quadratic forms over general fields 11E20: General ternary and quaternary quadratic forms; forms of more than two variables 57M25: Knots and links in S3 {For higher dimensions, see 57Q45} 57M50: Geometric structures on low-dimensional manifolds 57M60: Group actions in low dimensions
Subjects:Sciences > Mathematics > Topology
ID Code:29194
Deposited On:12 Mar 2015 09:45
Last Modified:12 Dec 2018 15:12

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