Twisted Bhargava cubes

Gan, Wee; Savin, Gordan

doi:10.2140/ant.2014.8.1913

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Twisted Bhargava cubes

Wee Teck Gan and Gordan Savin

Vol. 8 (2014), No. 8, 1913–1957

DOI: 10.2140/ant.2014.8.1913

Abstract

In his reinterpretation of Gauss’s composition law for binary quadratic forms, Bhargava determined the integral orbits of a prehomogeneous vector space which arises naturally in the structure theory of the split group ${Spin}_{8}$ . We consider a twisted version of this prehomogeneous vector space which arises in quasisplit ${Spin}_{8}^{E}$ , where $E$ is an étale cubic algebra over a field $F$ . We classify the generic orbits over $F$ by twisted composition $F$ -algebras of $E$ -dimension $2$ .

Keywords

Bhargava's cubes, twisted composition algebras

Mathematical Subject Classification 2010

Primary: 11S90

Secondary: 17A75, 17C40

Milestones

Received: 24 February 2014

Revised: 23 July 2014

Accepted: 26 July 2014

Published: 28 November 2014

Authors

Wee Teck Gan
Department of Mathematics National University of Singapore Block S17, 10 Lower Kent Ridge Road Ridge Road Singapore 119076 Singapore

Gordan Savin
Department of Mathematics University of Utah Salt Lake City, UT 84112 United States

Vol. 8, No. 8, 2014