Vol. 8, No. 8, 2014

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Twisted Bhargava cubes

Wee Teck Gan and Gordan Savin

Vol. 8 (2014), No. 8, 1913–1957

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 Spin8. We consider a twisted version of this prehomogeneous vector space which arises in quasisplit Spin8E, 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.

Bhargava's cubes, twisted composition algebras
Mathematical Subject Classification 2010
Primary: 11S90
Secondary: 17A75, 17C40
Received: 24 February 2014
Revised: 23 July 2014
Accepted: 26 July 2014
Published: 28 November 2014
Wee Teck Gan
Department of Mathematics
National University of Singapore
Block S17, 10 Lower Kent Ridge Road
Ridge Road
Singapore 119076
Gordan Savin
Department of Mathematics
University of Utah
Salt Lake City, UT 84112
United States