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Insights into Mathematics | Hypergroup definition and five key examples | Diffusion Symmetry 4 | N J Wildberger @njwildberger | Uploaded 2 years ago | Updated 16 hours ago
We state a precise definition of a finite commutative hypergroup, and then give five important classes of examples, 1) the class hypergroup of a finite (non-commutative) group G 2) the character hypergroup of a finite (non-commutative) group G 3) the hypergroup associated to a distance-transitive graph 4) double coset hypergroups arising from Gelfand pairs and 5) automorphism orbit hypergroups.

It will take some explaining to bring all these important families into proper focus, and show how they are useful potential tools for physicists and chemists trying to apply Diffusion Symmetry ideas to their subjects.

Video Contents (thanks to Lucas Lofaro)

0:00 Intro
0:08 Overview
0:58 Early History of Hypergoups
2:38 Definition of a Hypergroup
7:44 The Class Hypergroup of a Finite Group
9:59 The Character Hypergroup of a Finite Group
13:34 Hypergroup of a Distance-Transitive Graph
18:22 Double Coset Hpergroups
21:39 Automorphism Orbit Hypergroup
25:48 2D Representations of S3 Over a Finite Field

The Playlist for this series is at youtube.com/playlist?list=PLIljB45xT85Bmcc9ksBOAKgIZAl0BwPg7

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This is closely related to the Exceptional Structures in Mathematics and Physics lectures which are part of the Explore Research Level Mathematics video lectures. These are designed for motivated amateur, or professional, mathematicians wanting to delve into pure maths research without the abstraction and complexity that currently besets much of the subject. We will aim to always connect our abstract musings to computational reality by focusing on examples and explicit, concrete calculations --- naturally without any pretense of being "able to do an infinite number of things"!

To access more Explore Research Level Mathematics, please join Norman's Wild Egg Maths channel at youtube.com/channel/UCriFv3G22iOUidUhkIGXuhw, or become a Patron at patreon.com/njwildberger . There are already dozens of videos there, and many more will appear over the next months and years. One additional advantage: you get to access pdf summaries of some of the videos along with GeoGebra worksheets.

Here are the Insights into Mathematics Playlists:

youtube.com/playlist?list=PL55C7C83781CF4316
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Here are the Wild Egg Maths Playlists (some available only to Members!)

youtube.com/playlist?list=PLzdiPTrEWyz4rKFN541wFKvKPSg5Ea6XB
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youtube.com/playlist?list=PLzdiPTrEWyz4KD007Ge10dfrDVc4YwlYS
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Hypergroup definition and five key examples | Diffusion Symmetry 4 | N J Wildberger @njwildberger

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