#### Vol. 8, No. 8, 2014

 Download this article For screen For printing
 Recent Issues
 The Journal Cover Editorial Board Editors' Addresses Editors' Interests About the Journal Scientific Advantages Submission Guidelines Submission Form Subscriptions Editorial Login Contacts Author Index To Appear ISSN: 1944-7833 (e-only) ISSN: 1937-0652 (print)
Twisted Bhargava cubes

### Wee Teck Gan and Gordan Savin

Vol. 8 (2014), No. 8, 1913–1957
##### 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