Open Collections

Page Metadata

Item Metadata

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

Download

Media

48630-201809201701-MacDonald_lrv.mp4 [ 261.8MB ]

Metadata

JSON: 48630-1.0377184.json

JSON-LD: 48630-1.0377184-ld.json

RDF/XML (Pretty): 48630-1.0377184-rdf.xml

RDF/JSON: 48630-1.0377184-rdf.json

Turtle: 48630-1.0377184-turtle.txt

N-Triples: 48630-1.0377184-rdf-ntriples.txt

Original Record: 48630-1.0377184-source.json

Citation

48630-1.0377184.ris

Cite

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.

Include Metadata Specify width in pixels (leave blank for auto-width):

                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    

Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:

https://iiif.library.ubc.ca/presentation/dsp.48630.1-0377184/manifest

Comment

Related Items