Results 41 to 50 of about 12,045 (118)
Inductive constructions for Lie bialgebras and Hopf algebras
, 2006 In recent years, two generalisations of the theory of Lie algebras have become prominent, namely the "semi-classical" theory of Lie bialgebras and the "quantum" theory of Hopf algebras, including the quantized enveloping algebras.
Majid, Shahn +3 more
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Generalized q-oscillators and their Hopf structures
, 1995 In a recent paper Oh and Singh determined a Hopf structure for a generalized q-oscillator algebra. We prove that under some general assumptions, the latter is, apart from some algebras isomorphic to suq(2), su q(1,1), or their undeformed counterparts ...
Vansteenkiste, Nicolas +1 more
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The R-matrix action of untwisted affine quantum groups at roots of 1 [PDF]
, 2001 Let \hat{g} be an untwisted affine Kac–Moody algebra. The quantum group U_q(\hat{g}) is known to be a quasitriangular Hopf algebra (to be precise, a braided Hopf algebra).
GAVARINI, Fabio, Fabio Gavarini
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Comodule algebras and 2-cocycles over the (Braided) Drinfeld double
, 2019 We show that for dually paired bialgebras, every comodule algebra over one of the paired bialgebras gives a comodule algebra over their Drinfeld double via a crossed product construction.
Laugwitz, Robert
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Quantum double and multiparameter quantum groups
, 1994 After Drinfel'd and Jimbo's construction of quantized universal enveloping algebra associated to each complex simple Lie algebra, larger classes of quasitriangular Hopf algebras as been found and studied.
COSTANTINI, MAURO, Varagnolo M.
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Hopf algebra structure $H^{\sigma-R}$ with two sided invertible 2-cocycle
, 1999 summary:In this paper, we study the $H^{\sigma-R}$ type Hopf algebras and present its braided and quasitriangular Hopf algebra structure. This generalizes well-known results on $H^{\sigma }$ and $H^R$ type Hopf algebras. Finally, the classification of $H^
Wang, Shuanhong, Wang, Dingguo
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Lie algebras: infinite generalizations and deformations [PDF]
, 1990 There are many applications of Lie algebras to theoretical physics. This thesis is a study of some new mathematical structures which also are applicable to current physical ideas.
Fletcher, Paul, Fletcher, P
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Cross Products by Braided Groups and Bosonization
, 1994 Let H be a braided-cocommutative Hopf algebra in a braided monoidal category C and B a Hopf algebra in C on which H acts. We construct a cross product Hopf algebra B[formula]H in C.
Majid, S.
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EXTENDING ACTIONS OF HOPF ALGEBRAS TO ACTIONS OF THE DRINFEL'D DOUBLE [PDF]
, 2019 Mathematicians have long thought of symmetry in terms of actions of groups, but group actions have proven too restrictive in some cases to give an interesting picture of the symmetry of some mathematical objects, e.g. some noncommutative algebras.
Cline, Zachary Kirk
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Differential geometry on Hopf algebras and quantum groups [PDF]
, 1994 The differential geometry on a Hopf algebra is constructed, by using the basic axioms of Hopf algebras and noncommutative differential geometry. The space of generalized derivations on a Hopf algebra of functions is presented via the smash product, and ...
Watts, P.
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