Titlebook: Introduction to the Quantum Yang-Baxter Equation and Quantum Groups: An Algebraic Approach; Larry A. Lambe,David E. Radford Book 1997 Spri

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ntrol and systems engineering as well as in many of the related fields in which control is an enabling technology. The editors have assembled the most comprehensive reference possible, and this has been greatly facilitated by the publisher’s commitment continuously to publish updates to the articles

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Algebraic Preliminaries, 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 gener

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The Quantum Yang-Baxter Equation (QYBE),r 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 i

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Categories of Quantum Yang-Baxter Modules,ons 3.10 through 3.12 can be put in a more general context [Majid, 1994], [Pareigis, 1996]. A early treatment of the commutativity of an object in a category is given in [Eckmann and Hilton, 1962, p. 241].

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Quasitriangular Algebras, Bialgebras, Hopf Algebras and The Quantum Double,. See [Drinfel’d, 1987], [Drinfel’d, 1990], [Majid, 1990b], [Majid, 1991a], and [Radford, 1993b] for example. One of the most important examples of a quasitriangular Hopf algebra is the quantum double [Drinfel’d, 1987, p. 816]. In this chapter our focus will be on finite-dimensional objects. Every f

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Coquasitriangular Structures,ras. The FRT construction is the prime example of a coquasitriangular bialgebra. See [Faddeev et al., 1990], [Faddeev et al., 1989], and [Faddeev et al., 1988]. Typical references for coquasitriangular bialgebras include [Larson and Towber, 1991] and [Schauenburg, 1992a]. Also see [Majid, 1990b, Sec

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Some Classes of Solutions,r triangular solutions is made. The results of Section 2.11.2 are placed in a theoretical context. We apply some of the techniques developed in earlier chapters in Section 8.6.1 to find some one-parameter QYBE solutions.

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https://doi.org/10.1007/978-1-4615-4109-7algebra; computer; computer algebra; linear algebra; topology

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