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Essential dimension of Albert algebras

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Essential dimension of Albert algebras. / MacDonald, Mark.
In: Bulletin of the London Mathematical Society, 2014.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

MacDonald, M 2014, 'Essential dimension of Albert algebras', Bulletin of the London Mathematical Society. https://doi.org/10.1112/blms/bdu050

APA

MacDonald, M. (2014). Essential dimension of Albert algebras. Bulletin of the London Mathematical Society. https://doi.org/10.1112/blms/bdu050

Vancouver

MacDonald M. Essential dimension of Albert algebras. Bulletin of the London Mathematical Society. 2014. Epub 2014 Jun 20. doi: 10.1112/blms/bdu050

Author

MacDonald, Mark. / Essential dimension of Albert algebras. In: Bulletin of the London Mathematical Society. 2014.

Bibtex

@article{effcd0bcdfd14f259ffb54012132d62b,
title = "Essential dimension of Albert algebras",
abstract = "This paper shows that the number of independent parameters required to describe an Albert algebra up to isomorphism is at most seven. In other words, the essential dimension of the split group of type F 4 over a field of characteristic not 2 or 3 satisfies ed(F 4 )≤7 . This is achieved by reducing the structural group from the full 52-dimensional automorphism group to a subgroup of dimension 10, and exhibiting an eighteen-dimensional generically free linear representation that remains generically free once projectivized. ",
author = "Mark MacDonald",
year = "2014",
doi = "10.1112/blms/bdu050",
language = "English",
journal = "Bulletin of the London Mathematical Society",
issn = "0024-6093",
publisher = "Oxford University Press",

}

RIS

TY - JOUR

T1 - Essential dimension of Albert algebras

AU - MacDonald, Mark

PY - 2014

Y1 - 2014

N2 - This paper shows that the number of independent parameters required to describe an Albert algebra up to isomorphism is at most seven. In other words, the essential dimension of the split group of type F 4 over a field of characteristic not 2 or 3 satisfies ed(F 4 )≤7 . This is achieved by reducing the structural group from the full 52-dimensional automorphism group to a subgroup of dimension 10, and exhibiting an eighteen-dimensional generically free linear representation that remains generically free once projectivized.

AB - This paper shows that the number of independent parameters required to describe an Albert algebra up to isomorphism is at most seven. In other words, the essential dimension of the split group of type F 4 over a field of characteristic not 2 or 3 satisfies ed(F 4 )≤7 . This is achieved by reducing the structural group from the full 52-dimensional automorphism group to a subgroup of dimension 10, and exhibiting an eighteen-dimensional generically free linear representation that remains generically free once projectivized.

U2 - 10.1112/blms/bdu050

DO - 10.1112/blms/bdu050

M3 - Journal article

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

SN - 0024-6093

ER -