Quasitriangular Hopf algebra
In mathematics, a Hopf algebra, H, is quasitriangular if there exists an invertible element, R, of such that
* for all , where is the coproduct on H, and the linear map is given by ,
* ,
* , where , , and , where , , and , are algebra morphisms determined by R is called the R-matrix. As a consequence of the properties of quasitriangularity, the R-matrix, R, is a solution of the Yang-Baxter equation (and so a module V of H can be used to determine quasi-invariants of braids, knots and links). Also as a consequence of the properties of quasitriangularity, ; moreover , , and where (cf. Ribbon Hopf algebras).
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Quasitriangular Hopf algebra
In mathematics, a Hopf algebra, H, is quasitriangular if there exists an invertible element, R, of such that
* for all , where is the coproduct on H, and the linear map is given by ,
* ,
* , where , , and , where , , and , are algebra morphisms determined by R is called the R-matrix. As a consequence of the properties of quasitriangularity, the R-matrix, R, is a solution of the Yang-Baxter equation (and so a module V of H can be used to determine quasi-invariants of braids, knots and links). Also as a consequence of the properties of quasitriangularity, ; moreover , , and where (cf. Ribbon Hopf algebras).
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In mathematics, a Hopf algebra ...... d quantum double construction.
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In mathematics, a Hopf algebra ...... re (cf. Ribbon Hopf algebras).
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Quasitriangular Hopf algebra
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