Introduction to the World of Algebras

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Start date Jul 8, 2023
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Algebra Introduction Mathematics

In summary, Richard Pierce's book [2] aims to demonstrate that there is more to algebra than just Galois theory. He explains that although Galois theory may not be of interest to physicists, many other types of algebras are, such as tensor algebras, Banach algebras, Lie and Virasoro algebras, and supermanifolds. This article serves as a guide to the diverse world of algebras, introducing readers to famous mathematicians and physicists along the way.

Jul 8, 2023

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Introduction to the World of Algebras

Richard Pierce describes the intention of his book [2] about associative algebras as his attempt to prove that there is algebra after Galois theory. Whereas Galois theory might not really be on the agenda of physicists, many algebras are: from tensor algebras as the gown for infinitesimal coordinates over Graßmann and Banach algebras for the theory of differential forms and functions up to Lie and Virasoro algebras in quantum physics and supermanifolds. This article is meant to provide a guide and a presentation of the main parts of this zoo of algebras. And we will meet many famous mathematicians and physicists on the way.

Last edited: Aug 12, 2023