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Automorphism groups of triple systems and their generic subsystems MacDonald, Mark
Description
A vector space $V$ with a symmetric trilinear map $V\times V \times V \to V$ will be called a triple system. Freudenthal introduced and studied a certain type of triple system on a 56-dimensional vector space whose automorphism group is a simply connected group of type E$_7$. If $S$ is a subsystem generated by $n$ generic elements in a triple system $V$, then (in some situations) we can use the slice method to deduce a surjection from $\mathrm{Aut}(V,S)$-torsors to $\mathrm{Aut}(V)$-torsors. In this talk I will describe some examples of this procedure for triple systems of varying dimensions; in one example we will deduce the upper bound on essential dimension $\mathrm{ed}(\mathrm{HSpin}_{12}) \leq 6$ for characteristic not 2 (beating the previously best known bound of 26 from Garibaldi and Guralnick).
Item Metadata
Title |
Automorphism groups of triple systems and their generic subsystems
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2018-09-20T17:01
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Description |
A vector space $V$ with a symmetric trilinear map $V\times V \times V \to V$ will be called a triple system. Freudenthal introduced and studied a certain type of triple system on a 56-dimensional vector space whose automorphism group is a simply connected group of type E$_7$. If $S$ is a subsystem generated by $n$ generic elements in a triple system $V$, then (in some situations) we can use the slice method to deduce a surjection from $\mathrm{Aut}(V,S)$-torsors to $\mathrm{Aut}(V)$-torsors. In this talk I will describe some examples of this procedure for triple systems of varying dimensions; in one example we will deduce the upper bound on essential dimension
$\mathrm{ed}(\mathrm{HSpin}_{12}) \leq 6$ for characteristic not 2 (beating the previously best known bound of 26 from Garibaldi and Guralnick).
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Extent |
46.0
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Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: Lancaster University
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Series | |
Date Available |
2019-03-20
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0377184
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Aggregated Source Repository |
DSpace
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Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International