Chevalley groups of type $E_7$ in the 56-dimensional representation. (Q476673)

scientific article; zbMATH DE number 6375823

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English	Chevalley groups of type $E_7$ in the 56-dimensional representation.	scientific article; zbMATH DE number 6375823

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scholarly article

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title

Chevalley groups of type $E_7$ in the 56-dimensional representation. (English)

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Journal of Mathematical Sciences (New York)

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publication date

2 December 2014

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zbMATH Keywords

Chevalley groups over commutative rings

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minimal representations

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minimal modules

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MaRDI profile type

Publication

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full work available at URL

https://doi.org/10.1007/s10958-011-0641-y

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cites work

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Chevalley groups of type E7 in the 56-dimensional representation

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Some more exceptional numerology.

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Normalizer of the Chevalley group of type ${\mathrm E}_6$

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Elementary subgroup of an isotropic reductive group is perfect.

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Elementary subgroups of isotropic reductive groups

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Surjective stability for the $K_ 1$-functor for some exponential Chevalley groups

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Chevalley groups over local rings

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Whitehead groups of chevalley groups over polynomial rings

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On normal subgroups of Chevalley groups over commutative rings

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Some multilinear forms with large isometry groups

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On the structure of parabolic subgroups

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The octonions

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Localization-completion strikes again: relative $K_1$ is nilpotent by Abelian

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A NEW TYPE OF NON ASSOCIATIVE ALGEBRAS

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A minimal representation for the Lie algebra $E_ 7$

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Groups of type E7.

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Minimal representations of E6, E7, and E8 and the generalized Capelli identity.

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Quantum cohomology of minuscule homogeneous spaces

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Homology of the double and the triple loop spaces of $E_6$, $E_7$ and $E_8$

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The kernel of the Rost invariant, Serre's conjecture II and the Hasse principle for quasi-split groups $^{3,6}D_4$, $E_6$, $E_7$.

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Q3135194

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Computing in groups of Lie type

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The fifty-six-dimensional module for $E_ 7$. I: A four form for $E_ 7$

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A characterization of quadratic forms of type $E_6$, $E_7$, and $E_8$

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Explicit Cayley triples in real forms of $E_ 7$.

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The closure diagram for nilpotent orbits of the split real form of ${E_7}$

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A Geometry for E 7

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Exceptional Lie Algebras and Related Algebraic and Geometric Structures

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Strictly Regular Elements in Freudenthal Triple Systems

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On the classification of Freudenthal triple systems and Lie algebras of type $E_7$

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Basic representations of affine Lie algebras and dual resonance models

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Oktaven, Ausnahmegruppen und Oktavengeometrie

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Isotropic trialitarian algebraic groups

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GROUPS OF TYPEE7OVER ARBITRARY FIELDS

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Unramified cohomology of classifying varieties for exceptional simply connected groups

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Some representations of exceptional Lie algebras

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On standard L-functions for E6 and E7.

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Embeddings of $U_ 3(8)$, $Sz(8)$ and the Rudvalis group in algebraic groups of type $E_ 7$

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On the lattice of subgroups of chevalley groups containing a split maximal torus

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Some Irreducible Representations of Exceptional Algebraic Groups

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Relative subgroups in Chevalley groups

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Relative commutator calculus in Chevalley groups.

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Matrix generators for exceptional groups of Lie type

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Projective geometry of Freudenthal's varieties of certain type

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Kostant's conjecture holds for $E_ 7$: $L_ 2(37)<E_ 7(\mathbb{C})$

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HS <E 7 (5)

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The projective geometry of Freudenthal's magic square.

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A System of Quadrics Describing the Orbit of the Highest Weight Vector

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The conjugate classes of unipotent elements of the Chevalley groups $E_ 7$ and $E_ 8$.

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The $({\bf A_2,G_2})$ duality in ${\bf E_6}$, octonions and the triality principle

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Identification of matrix generators of a Chevalley group.

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Constructions for octonion and exceptional Jordan algebras

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Configurations of seven lines on the real projective plane and the root system of type $E_7$

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Q3892350

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Embeddings and hyperplanes of the Lie incidence geometry of type $E_{7,1}$

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Some Groups of Type E7

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Normal Structure of Maximal Parabolic Subgroups in Chevalley Groups over Rings

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Generators, Relations and Coverings of Chevalley Groups Over Commutative Rings

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On normal subgroups of Chevalley groups over commutative rings

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A third look at weight diagrams

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AN A3-PROOF OF STRUCTURE THEOREMS FOR CHEVALLEY GROUPS OF TYPES E6 AND E7

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Chevalley groups over commutative rings. I: Elementary calculations

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Moufang quadrangles of type E 6 and E 7

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Identifiers

zbMATH Open document ID

1306.20050

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Mathematics Subject Classification ID

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10.1007/S10958-011-0641-Y

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Sitelinks

Mathematics(1 entry)

mardi Publication:476673

Chevalley groups of type \(E_7\) in the 56-dimensional representation. (Q476673)

Statements

Identifiers

Sitelinks

Mathematics(1 entry)