Hiroshima Mathematical Journal

Addendum to ‘‘On integral quadratic forms having commensurable groups of automorphisms’’

José María Montesinos-Amilibia

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Abstract

Cassels proved that projectively equivalent integral quadratic forms are commensurable. In this note, an elementary proof of the converse of this theorem, for indefinite forms, is given. This was proved in "On integral quadratic forms having commensurable groups of automorphisms," Hiroshima Math. J. 43, 371–411 (2013) for forms of Sylvester signature +++. . .+- or ---. . .-+ (hyperbolic forms) and it was left there, as an open problem, for non-hyperbolic indefinite forms of any Sylvester signature.

Article information

Source
Hiroshima Math. J., Volume 44, Number 3 (2014), 341-350.

Dates
First available in Project Euclid: 26 December 2014

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1419619751

Digital Object Identifier
doi:10.32917/hmj/1419619751

Mathematical Reviews number (MathSciNet)
MR3296080

Zentralblatt MATH identifier
1315.11023

Subjects
Primary: 11E04: Quadratic forms over general fields 11E20: General ternary and quaternary quadratic forms; forms of more than two variables 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57M50: Geometric structures on low-dimensional manifolds 57M60: Group actions in low dimensions

Keywords
Integral quadratic form automorph commensurability class

Citation

Montesinos-Amilibia, José María. Addendum to ‘‘On integral quadratic forms having commensurable groups of automorphisms’’. Hiroshima Math. J. 44 (2014), no. 3, 341--350. doi:10.32917/hmj/1419619751. https://projecteuclid.org/euclid.hmj/1419619751


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See also

  • See: José María Montesinos-Amilibia. On integral quadratic forms having commensurable groups of automorphisms. Hiroshima Math. J., vol. 43, no. 3 (2013), pp. 371-411.