Results 11 to 20 of about 12,045 (118)
Local Quasitriangular Hopf Algebras [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2008 We find a new class of Hopf algebras, local quasitriangular Hopf algebras, which generalize quasitriangular Hopf algebras. Using these Hopf algebras, we obtain solutions of the Yang-Baxter equation in a systematic way. The category of modules with finite
Shouchuan Zhang +2 more
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Quasitriangular Hopf group algebras and braided monoidal categories [PDF]
Czechoslovak Mathematical Journal, 2014 Throughout this review, \(\pi\) denotes a discrete group with neutral element \(1\), and \(k\) denotes a field. All considered vector spaces and tensor products are assumed to be over \(k\). A \(\pi\)-algebra \(H=\{H_\alpha\}_{\alpha\in\pi}\) with multiplication \(m=\{m_{\alpha,\beta}\colon H_\alpha\otimes H_\beta\to H_{\alpha\beta}\}_{\alpha,\beta\in ...
Shiyin Zhao, Jing Wang, Hui-xiang Chen
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The Brauer group of some quasitriangular Hopf algebras [PDF]
Journal of Algebra, 2003 Let \(k\) be a field and \(H\) a Hopf algebra with bijective antipode. Then we can introduce the Brauer group \(BQ(k,H)\) of Yetter-Drinfeld module algebras [see \textit{S. Caenepeel, F. Van Oystaeyen} and \textit{Y. H. Zhang}, Trans. Am. Math. Soc. 349, No. 9, 3737-3771 (1997; Zbl 0912.16015)].
G. Carnovale, J. Cuadra
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A nonlinear deformed su(2) algebra with a two-color quasitriangular Hopf structure [PDF]
, 1997 Nonlinear deformations of the enveloping algebra of su(2), involving two arbitrary functions of J0 and generalizing the Witten algebra, were introduced some time ago by Delbecq and Quesne. In the present paper, the problem of endowing some of them with a
D. Bonatsos +4 more
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Quasitriangular (G-cograded) multiplier Hopf algebras
Journal of Algebra, 2005 We put the known results on the antipode of a usual quasitriangular Hopf algebra into the framework of multiplier Hopf algebras. We illustrate with examples which can not be obtained using classical Hopf Algebras. The focus of the present paper lies on the class of the so-called group cograded multiplier Hopf algebras. By doing so, we bring the results
Delvaux, L., Van Daele, A., Wang, S.H.
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Braided Lie algebras and bicovariant differential calculi over co-quasitriangular Hopf algebras [PDF]
, 2001 We show that if gΓ is the quantum tangent space (or quantum Lie algebra in the sense of Woronowicz) of a bicovariant first-order differential calculus over a co-quasitriangular Hopf algebra (A,r), then a certain extension of it is a braided Lie algebra ...
X. Gomez, Shahn Majid
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A CLASS OF QUASITRIANGULAR GROUP-COGRADED MULTIPLIER HOPF ALGEBRAS [PDF]
Glasgow Mathematical Journal, 2018 For a multiplier Hopf algebra pairing 〈A,B〉, we construct a class of group-cograded multiplier Hopf algebras D(A,B), generalizing the classical construction of finite dimensional Hopf algebras introduced by Panaite and Staic Mihai [Isr. J. Math.
Tao Yang, Xuan Zhou, Hai-xing Zhu
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Quasitriangular and Differential Structures on Bicrossproduct Hopf Algebras
Journal of Algebra, 1999 38 pages latex, no ...
Beggs, Edwin, Majid, Shahn
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Hopf modules in the braided monoidal category $_LM$
Le Matematiche, 2011 Suppose that L is a quasitriangular weak Hopf algebra with a bijective antipode and H is a weak Hopf algebra in the braided nonoidal category LM. We prove that the fundamental theorem for right H-Hopf modules in LM.
Yin Yanmin, Zhang Mingchuan
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Quasitriangular coideal subalgebras of Uq(g) in terms of generalized Satake diagrams
Bulletin of the London Mathematical Society, Volume 52, Issue 4, Page 693-715, August 2020., 2020 Abstract Let g be a finite‐dimensional semisimple complex Lie algebra and θ an involutive automorphism of g. According to Letzter, Kolb and Balagović the fixed‐point subalgebra k=gθ has a quantum counterpart B, a coideal subalgebra of the Drinfeld–Jimbo quantum group Uq(g) possessing a universal K‐matrix K.
Vidas Regelskis, Bart Vlaar
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