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Automorphism groups of triple systems and their generic subsystems MacDonald, Mark Sep 20, 2018
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Title | Automorphism groups of triple systems and their generic subsystems |
Creator |
MacDonald, Mark |
Publisher | Banff International Research Station for Mathematical Innovation and Discovery |
Date Issued | 2018-09-20T17:01 |
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). |
Extent | 46.0 |
Subject |
Mathematics Algebraic geometry Group theory and generalizations |
Geographic Location | Banff (Alta.) |
Type |
Moving Image |
FileFormat | video/mp4 |
Language | eng |
Notes | Author affiliation: Lancaster University |
Series | BIRS Workshop Lecture Videos (Banff, Alta) |
Date Available | 2019-03-20 |
Provider | Vancouver : University of British Columbia Library |
Rights | Attribution-NonCommercial-NoDerivatives 4.0 International |
DOI | 10.14288/1.0377184 |
URI | http://hdl.handle.net/2429/68954 |
Affiliation |
Non UBC |
Peer Review Status | Unreviewed |
Scholarly Level | Faculty |
Rights URI | http://creativecommons.org/licenses/by-nc-nd/4.0/ |
AggregatedSourceRepository | DSpace |
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https://iiif.library.ubc.ca/presentation/dsp.48630.1-0377184/manifest