Klassifizierung der alternierenden Gröszen dritten Grades in 7 Dimensionen

Schouten, J. A.

doi:10.1007/bf03016791

Cited by 49 publications

(38 citation statements)

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“…The classification in this case was carried out by J.A. SCHOUTEN [7] in 1931 for F = C, and, independently, by CRESP [3] in 1976 for F algebraically closed of characteristic i=2,3. GUREVICH [5] gives an answer to the classification problem with F =C, r = 3 and n = 8.…”

Section: (3)mentioning

confidence: 99%

Trilinear alternating forms on a vector space of dimension 7

Cohen¹,

Helminck²

1988

Communications in Algebra

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Section: (3)mentioning

confidence: 99%

Trilinear alternating forms on a vector space of dimension 7

Cohen¹,

Helminck²

1988

Communications in Algebra

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“…We also have that any symplectic algebra that is abelian-by-nilpotent must be nilpotent while this is not the case in general for solvable algebras. We should also mention here that the study of orbits in ∧ 3 V is a classical problem that has been considered by a number of people (see for example [2,5,6]). …”

Section: Introductionmentioning

confidence: 98%

On simple symplectic alternating algebras and their groups of automorphisms

Puglisi

Traustason

2016

Journal of Algebra

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Let N be any perfect symplectic alternating algebra. We show that N can be embedded into a larger simple alternating algebra S of dimension 7 · (dim N ) + 6 such that Aut (S) = {id}. This answers a question raised in [9]. Building on this result we show moreover that for any finite group G and characteristic c there exists a symplectic alternating algebra L over a field F of characteristic c such that Aut (L) = G.

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“…[3,5]. For group modules involving a general linear group GL(V ) acting on an exterior power of V , we also have a number of results dealing with the classification of orbits on vectors, see [2,4,18,21,22,23,28,29,30,32,33,34]. Some of these results however impose certain restrictions on the underlying field.…”

Section: Introductionmentioning

confidence: 99%

A 14-dimensional Module for the Symplectic Group: Orbits on Vectors

Bruyn

Kwiatkowski

2015

Communications in Algebra

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Let F be a field, V a 6-dimensional F-vector space and f a nondegenerate alternating bilinear form on V . We consider a 14-dimensional module for the symplectic group Sp(V, f ) ∼ = Sp(6, F) associated with (V, f ), and classify the orbits on vectors. For characteristic distinct from 2, this module is irreducible and isomorphic to the Weyl module of Sp(V, f ) for the fundamental weight λ 3 . If the characteristic is 2, then the module is reducible as it contains an 8-dimensional submodule isomorphic to the spin module of Sp(V, f ).

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Klassifizierung der alternierenden Gröszen dritten Grades in 7 Dimensionen

Cited by 49 publications

References 1 publication

Trilinear alternating forms on a vector space of dimension 7

Trilinear alternating forms on a vector space of dimension 7

On simple symplectic alternating algebras and their groups of automorphisms

A 14-dimensional Module for the Symplectic Group: Orbits on Vectors

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