Difference between revisions of "Video/What is...representation theory?"

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  ...it is now '''more true''' to say that for further advances in the abstract theory one must look largely to the representation of a group as a group of linear substitutions.
  ...it is now '''more true''' to say that for further advances in the abstract theory one must look largely to the representation of a group as a group of linear substitutions.


It would be useful to watch the video from [https://youtu.be/VYzhA_nj0sU?t=1017 here].
It would be useful to watch the video from [https://youtu.be/VYzhA_nj0sU?t=1000 here].
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=References=
=References=

Revision as of 23:28, 29 March 2022

Tubbenhauer, Daniel (Mar 30, 2022). What is...representation theory?. local page: VisualMath. 


{{#ev:youtube |VYzhA_nj0sU }}

According to this video, the main thesis of Representation Theory is the linear approximation of algebraic objects. It would be useful to refer to the Semi-tensor product(STP) as developed by Daizhan Cheng. See following references:

  1. Analysis and Control of Boolean Networks A Semi-tensor Product Approach[1]
  2. A BRIEF TUTORIAL EXPOSITION OF SEMI-TENSOR PRODUCTS OF MATRICES[2]

Theory of Groups of Finite Order

The end of this video extensively discusses the idea of William Burnside's work on Theory of Groups of Finite Order[3]. The critical message can be summarized in the second version (published in 1911, which stated the following message: 

...it is now more true to say that for further advances in the abstract theory one must look largely to the representation of a group as a group of linear substitutions.

It would be useful to watch the video from here. {{#ev:youtube |VYzhA_nj0sU|||||start=1000 }}

References

  1. ↑ Cheng, Daizhan; Qi, Hongsheng; Li, Zhiqiang (2011). Analysis and Control of Boolean Networks:A Semi-tensor Product Approach. local page: Springer-Verlag. ISBN 978-0-85729-097-7. 
  2. ↑ Rushdi, Ali Muhammad; Ghaleb, Fares (August 28, 2017). "A BRIEF TUTORIAL EXPOSITION OF SEMI-TENSOR PRODUCTS OF MATRICES". local page: Research Gate. 
  3. ↑ Burnside, William (1897). Theory of Groups of Finite Order. local page: Cambridge University Press. 

Related Pages

VisualMath

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