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2006 Some groups of type $E_{7}$
T. A. Springer
Nagoya Math. J. 182: 259-284 (2006).

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.

Citation

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T. A. Springer. "Some groups of type $E_{7}$." Nagoya Math. J. 182 259 - 284, 2006.

Information

Published: 2006
First available in Project Euclid: 20 June 2006

zbMATH: 1160.20044
MathSciNet: MR2235344

Subjects:
Primary: 20G10, 20G15

Rights: Copyright © 2006 Editorial Board, Nagoya Mathematical Journal

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