On the braiding on a Hopf algebra in a braided category.
Schauenburg, Peter (1998)
The New York Journal of Mathematics [electronic only]
Similarity:
Schauenburg, Peter (1998)
The New York Journal of Mathematics [electronic only]
Similarity:
Józef Słomiński (1980)
Colloquium Mathematicae
Similarity:
R. Kiełpiński (1978)
Colloquium Mathematicae
Similarity:
Hans-E. Porst, Manfred B. Wischnewski (1978)
Manuscripta mathematica
Similarity:
Yuanyuan Chen, Zhongwei Wang, Liangyun Zhang (2014)
Colloquium Mathematicae
Similarity:
A twisted generalization of quasitriangular Hopf algebras called quasitriangular Hom-Hopf algebras is introduced. We characterize these algebras in terms of certain morphisms. We also give their equivalent description via a braided monoidal category . Finally, we study the twisting structure of quasitriangular Hom-Hopf algebras by conjugation with Hom-2-cocycles.
José N. Alonso Alvarez, José Manuel Fernández Vilaboa, Ramón González Rodríguez (2001)
Publicacions Matemàtiques
Similarity:
Let τ be an invertible skew pairing on (B,H) where B and H are Hopf algebras in a symmetric monoidal category C with (co)equalizers. Assume that H is quasitriangular. Then we obtain a new algebra structure such that B is a Hopf algebra in the braided category γD and there exists a Hopf algebra isomorphism w: B ∞ H → B [×] H in C, where B ∞ H is a Hopf algebra with (co)algebra structure the smash (co)product and B [×] H is the Hopf algebra defined by Doi and Takeuchi. ...
Kandelaki, Tamaz (2000)
Homology, Homotopy and Applications
Similarity:
Xiaofan Zhao, Xiaohui Zhang (2016)
Colloquium Mathematicae
Similarity:
We introduce the notion of a lazy 2-cocycle over a monoidal Hom-Hopf algebra and determine all lazy 2-cocycles for a class of monoidal Hom-Hopf algebras. We also study the extension of lazy 2-cocycles to a Radford Hom-biproduct.
Majid, Shahn
Similarity:
[For the entire collection see Zbl 0742.00067.]The Tanaka-Krein type equivalence between Hopf algebras and functored monoidal categories provides the heuristic strategy of this paper. The author introduces the notion of a double cross product of monoidal categories as a generalization of double cross product of Hopf algebras, and explains some of the motivation from physics (the representation theory for double quantum groups).The Hopf algebra constructions are formulated in terms of...
Sung Sa Hong, Louis D. Nel (1979)
Mathematische Zeitschrift
Similarity:
Takeshi Katsura, Paul S. Muhly, Aidan Sims, Mark Tomforde (2008)
Studia Mathematica
Similarity:
Given an ultragraph in the sense of Tomforde, we construct a topological quiver in the sense of Muhly and Tomforde in such a way that the universal C*-algebras associated to the two objects coincide. We apply results of Muhly and Tomforde for topological quiver algebras and of Katsura for topological graph C*-algebras to study the K-theory and gauge-invariant ideal structure of ultragraph C*-algebras.
Šlapal, Josef (1996)
Mathematica Pannonica
Similarity:
Kazunori Kodaka, Tamotsu Teruya (2015)
Studia Mathematica
Similarity:
Following Jansen and Waldmann, and Kajiwara and Watatani, we introduce notions of coactions of a finite-dimensional C*-Hopf algebra on a Hilbert C*-bimodule of finite type in the sense of Kajiwara and Watatani and define their crossed product. We investigate their basic properties and show that the strong Morita equivalence for coactions preserves the Rokhlin property for coactions of a finite-dimensional C*-Hopf algebra on unital C*-algebras.
Sergei S. Akbarov
Similarity:
An envelope in a category is a construction that generalizes the operations of "exterior completion", like completion of a locally convex space, or the Stone-Čech compactification of a topological space, or the universal enveloping algebra of a Lie algebra. Dually, a refinement generalizes the operations of "interior enrichment", like bornologification (or saturation) of a locally convex space, or simply connected covering of a Lie group. In this paper we define envelopes and refinements...
Michihisa Wakui (2003)
Banach Center Publications
Similarity:
We determine the coribbon structures of some finite dimensional braided Hopf algebras generated by 2×2-matrix coalgebras constructed by S. Suzuki. As a consequence, we see that such a Hopf algebra has a coribbon structure if and only if it is of Kac-Paljutkin type.
Volodymyr Lyubashenko (1997)
Banach Center Publications
Similarity:
Given an abelian 𝑉-linear rigid monoidal category 𝑉, where 𝑉 is a perfect field, we define squared coalgebras as objects of cocompleted 𝑉 ⨂ 𝑉 (Deligne's tensor product of categories) equipped with the appropriate notion of comultiplication. Based on this, (squared) bialgebras and Hopf algebras are defined without use of braiding. If 𝑉 is the category of 𝑉-vector spaces, squared (co)algebras coincide with conventional ones. If 𝑉 is braided, a braided Hopf algebra can be obtained...