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Algebra

In: Topics in Physical Mathematics

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  • Kishore Marathe

    (City University of New York Brooklyn College)

Abstract

We suppose that the reader is familiar with basic structures of algebra such as groups, rings, fields, and vector spaces and their morphisms, as well as the elements of representation theory of groups. Theory of groups was discovered by Cauchy. He called it “theory of substitutions.” He found it so exotic that he is said to have remarked: “It is a beautiful toy, but it will not have any use in the mathematical sciences.” In fact, quite the opposite was revealed to be true. The concept of group has proved to be fundamental in all mathematical sciences. In particular, the theory of Lie groups enjoys wide applicability in theoretical physics. We will discuss Lie groups in Chapter 3. Springer has started to reissue the volumes originally published under the general title “Éléments de mathématique” by Nicholas Bourbaki (see the note in Appendix B). The volumes dealing with Lie groups and Lie algebras are [57, 56]. They can be consulted as standard reference works, even though they were written more than 20 years ago.

Suggested Citation

  • Kishore Marathe, 2010. "Algebra," Springer Books, in: Topics in Physical Mathematics, chapter 0, pages 1-32, Springer.
    • Handle: RePEc:spr:sprchp:978-1-84882-939-8_1
    DOI: 10.1007/978-1-84882-939-8_1
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