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Norms in quadratic fields and their relations to non commuting 2×2 matrices I

Taussky, Olga (1976) Norms in quadratic fields and their relations to non commuting 2×2 matrices I. Monatshefte für Mathematik, 82 (3). pp. 253-255. ISSN 0026-9255. https://resolver.caltech.edu/CaltechAUTHORS:20201013-104023229

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Abstract

Let A be a fixed 2×2 integral matrix with irrational characteristic roots. Let B be an arbitrary 2×2 integral matrix. It was previously shown that -det (AB-BA) = norm λ, where λ is in the field of the characteristic roots of A. It is now shown that the λ's corresponding to varying B's can be chosen to form a fractional ideal in this field.


Item Type:Article
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https://doi.org/10.1007/bf01526330DOIArticle
https://rdcu.be/b8sIxPublisherFree ReadCube access
Additional Information:© 1976 Springer. (Received 31 October 1975) Dedicated to Prof. Dr. E. Hlawka on the occasion of his 60th birthday. This work was carried out (in part) under an NSF grant.
Funders:
Funding AgencyGrant Number
NSFUNSPECIFIED
Subject Keywords:Explicit Construction; Characteristic Root; Integral Ideal; Quadratic Field; Ideal Matrice
Issue or Number:3
Record Number:CaltechAUTHORS:20201013-104023229
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20201013-104023229
Official Citation:Taussky, O. Norms in quadratic fields and their relations to non commuting 2×2 matrices I. Monatshefte für Mathematik 82, 253–255 (1976). https://doi.org/10.1007/BF01526330
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:106019
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:13 Oct 2020 18:18
Last Modified:13 Oct 2020 18:18

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