Vol. 8, No. 8, 2014

Download this article
Download this article For screen
For printing
Recent Issues

Volume 10
Issue 9, 1845–2052
Issue 8, 1601–1843
Issue 7, 1373–1600
Issue 6, 1147–1371
Issue 5, 939–1146
Issue 4, 695–938
Issue 3, 451–694
Issue 2, 215–450
Issue 1, 1–214

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 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 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.

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