Abstract
In this chapter we develop the theory of coalgebras, bialgebras, Hopf algebras, and their associated representations which is needed for our treatment of algebraic structures related to the quantum Yang-Baxter equation. Many exercises of various degrees of difficulty are provided to help the reader understand the concepts introduced. We provide a complete and self contained treatment of the topics mentioned above for our purposes. There are general references on coalgebras, bialgebras, and Hopf algebras which the reader may find useful to consult Abe, 1980, [Heyneman and Sweedler, 1969], and [Heyneman and Sweedler, 1970], [Montgomery, 1993], and [Sweedler, 1969].
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© 1997 Springer Science+Business Media Dordrecht
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Lambe, L.A., Radford, D.E. (1997). Algebraic Preliminaries. In: Introduction to the Quantum Yang-Baxter Equation and Quantum Groups: An Algebraic Approach. Mathematics and Its Applications, vol 423. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-4109-7_1
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DOI: https://doi.org/10.1007/978-1-4615-4109-7_1
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-6842-7
Online ISBN: 978-1-4615-4109-7
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