Algebra & Number Theory

Twisted Bhargava cubes

Wee Gan and Gordan Savin

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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.

Article information

Algebra Number Theory, Volume 8, Number 8 (2014), 1913-1957.

Received: 24 February 2014
Revised: 23 July 2014
Accepted: 26 July 2014
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11S90: Prehomogeneous vector spaces
Secondary: 17A75: Composition algebras 17C40: Exceptional Jordan structures

Bhargava's cubes twisted composition algebras


Gan, Wee; Savin, Gordan. Twisted Bhargava cubes. Algebra Number Theory 8 (2014), no. 8, 1913--1957. doi:10.2140/ant.2014.8.1913.

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