Abstract
As mentioned in the Introduction, the quantum Yang-Baxter equation arises in variety of contexts and has a number of forms. In this chapter we consider three fundametnal forms of the equation: the constant, the one-parmaeter; and the two-parameter. The constant and one-parameter forms are connected to bialgebras through the FRT construction. We introduce the FRT construction in this chapter. The constant form of the quantum Yang-Baxter equation is very closely related to the braid equation, an equation of considerable importance for invariants of knots and links. Our treatment of compatibility conditions in the constant case is based on [Lambe, 1994] and [Lambe and Radford, 1993]. Our treatment of symmetries inSection 2.3 is based on [Hietarinta, 1993b, Section 2]. From this point on in the text we will refer to the quantum Yang-Baxter equation as the QYBE.
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© 1997 Springer Science+Business Media Dordrecht
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Lambe, L.A., Radford, D.E. (1997). The Quantum Yang-Baxter Equation (QYBE). 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_2
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DOI: https://doi.org/10.1007/978-1-4615-4109-7_2
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-6842-7
Online ISBN: 978-1-4615-4109-7
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