Difference between revisions of "Video/What is...representation theory?"
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=Theory of Groups of Finite Order= | =Theory of Groups of Finite Order= | ||
The end of this video extensively discusses the idea of [[William Burnside]]'s work on [[Book/Theory of Groups of Finite Order|Theory of Groups of Finite Order]]<ref>{{:Book/Theory of Groups of Finite Order}}</ref>. | The end of this video extensively discusses the idea of [[William Burnside]]'s work on [[Book/Theory of Groups of Finite Order|Theory of Groups of Finite Order]]<ref>{{:Book/Theory of Groups of Finite Order}}</ref>. 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. | |||
=References= | =References= | ||
Revision as of 23:27, 29 March 2022
Tubbenhauer, Daniel (Mar 30, 2022). What is...representation theory?. local page: VisualMath.
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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:
- Analysis and Control of Boolean Networks A Semi-tensor Product Approach[1]
- 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.
References
- ↑ 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.
- ↑ Rushdi, Ali Muhammad; Ghaleb, Fares (August 28, 2017). "A BRIEF TUTORIAL EXPOSITION OF SEMI-TENSOR PRODUCTS OF MATRICES". local page: Research Gate.
- ↑ Burnside, William (1897). Theory of Groups of Finite Order. local page: Cambridge University Press.