Journal ArticleDOI
Two dual classes of bialgebras related to the concepts of “quantum group” and “quantum lie algebra”
Richard G. Larson,Towber Jacob +1 more
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In this article, two dual classes of bialgebras related to the concepts of quantum group and quantum lie algebra are introduced, and they are shown to have similar properties to our dual classes.Citations
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Algebras and Hopf Algebras in Braided Categories
TL;DR: In this article, the authors introduce algebraists to the theory of Hopf algebras in braided categories, including the notion of ''brided-commutative'' or ''braided-cocommutative' Hopf groups.
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Multiplication alteration by two-cocycles - the quantum version
Yukio Doi,Mitsuhiro Takeuch +1 more
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Braided bialgebras and quadratic blalgebras
TL;DR: In this paper, Braided bialgebras and quadratic blalges are used to construct a set of Braided Braided Bialges and Quadratic Blalges.
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The Hom–Yang–Baxter equation, Hom–Lie algebras, and quasi-triangular bialgebras
TL;DR: In this paper, a twisted version of the Yang-Baxter equation, called the Hom-Yang -Baxter Equation (HYBE), is studied, motivated by Hom-Lie algebras.
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Yetter-Drinfel'd categories associated to an arbitrary bialgebra
David E. Radford,Jacob Towber +1 more
TL;DR: In this paper, various prebraided monoidal categories associated to a bialgebra over a commutative ring are studied and their relationships at various levels are examined and generalizations of braided bialgebras are described and associated with them.
References
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Journal ArticleDOI
Quantum field theory and the Jones polynomial
TL;DR: In this paper, it was shown that 2+1 dimensional quantum Yang-Mills theory with an action consisting purely of the Chern-Simons term is exactly soluble and gave a natural framework for understanding the Jones polynomial of knot theory in three dimensional terms.
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A q -difference analogue of U(g) and the Yang-Baxter equation
TL;DR: Aq-difference analogue of the universal enveloping algebra U(g) of a simple Lie algebra g is introduced in this article, and its structure and representations are studied in the simplest case g=sl(2).
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A polynomial invariant for knots via von Neumann algebras
TL;DR: In this paper, it was shown that (6, n) and (c, ra) represent the same closed braid (up to link isotopy) if and only if they are equivalent for the equivalence relation generated by Markov moves of types 1 and 2 on the disjoint union of the braid groups.
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Invariants of 3-manifolds via link polynomials and quantum groups
TL;DR: In this paper, the authors construct topological invariants of compact oriented 3-manifolds and of framed links in such manifolds, where the terms of the sequence are equale to the values of the Jones polynomial of the link in the corresponding roots of 1.