Nagoya Mathematical Journal

Some groups of type $E_{7}$

T. A. Springer

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Abstract

An algebraic group of type $E_{7}$ over an algebraically closed field has an irreducible representation in a vector space of dimension $56$ and is, in fact, the identity component of the automorphism group of a quartic form on the space. This paper describes the construction of the quartic form if the characteristic is $\neq 2, 3$, taking into account a field of definition $F$. Certain $F$-forms of $E_{7}$ appear in the automorphism groups of quartic forms over $F$, as well as forms of $E_{6}$. Many of the results of the paper are known, but are perhaps not easily accessible in the literature.

Article information

Source
Nagoya Math. J., Volume 182 (2006), 259-284.

Dates
First available in Project Euclid: 20 June 2006

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1150810009

Mathematical Reviews number (MathSciNet)
MR2235344

Zentralblatt MATH identifier
1160.20044

Subjects
Primary: 20G15: Linear algebraic groups over arbitrary fields 20G10: Cohomology theory

Citation

Springer, T. A. Some groups of type $E_{7}$. Nagoya Math. J. 182 (2006), 259--284. https://projecteuclid.org/euclid.nmj/1150810009


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