Topic
Quasitriangular Hopf algebra
About: Quasitriangular Hopf algebra is a research topic. Over the lifetime, 2357 publications have been published within this topic receiving 61290 citations.
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Book•
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04 Nov 1994
TL;DR: In this paper, the authors introduce the theory of quantum groups with emphasis on the spectacular connections with knot theory and Drinfeld's recent fundamental contributions and present the quantum groups attached to SL2 as well as the basic concepts of the Hopf algebras.
Abstract: Here is an introduction to the theory of quantum groups with emphasis on the spectacular connections with knot theory and Drinfeld's recent fundamental contributions. It presents the quantum groups attached to SL2 as well as the basic concepts of the theory of Hopf algebras. Coverage also focuses on Hopf algebras that produce solutions of the Yang-Baxter equation and provides an account of Drinfeld's elegant treatment of the monodromy of the Knizhnik-Zamolodchikov equations.
5,966 citations
Book•
01 Jan 1993TL;DR: In this paper, the authors define integrals and semisimplicity of subalgebras, and define a set of properties of finite-dimensional Hopf algebra and smash products.
Abstract: Definitions and examples Integrals and semisimplicity Freeness over subalgebras Action of finite-dimensional Hopf algebras and smash products Coradicals and filtrations Inner actions Crossed products Galois extensions Duality New constructions from quantum groups Some quantum groups.
2,659 citations
Book•
01 Apr 2000TL;DR: In this paper, the authors define Hopf algebras as "quasitriangular Hopf-algebraes" and introduce matrix quantum groups and bicrossproduct hopf alges.
Abstract: Introduction 1. Definition of Hopf algebras 2. Quasitriangular Hopf algebras 3. Quantum enveloping algebras 4. Matrix quantum groups 5. Quantum random walks and combinatorics 6. Bicrossproduct Hopf algebras 7. Quantum double and double cross products 8. Lie bialgebras and Poisson brackets 9. Representation theory 10. Braided groups and q-deformation References Symbols Indexes.
2,219 citations
Journal Article•
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TL;DR: In this article, the fundamental isomorphism theorem of π-algebras is proved and some algebraic properties of Hopf π algebbras are studied.
Abstract: This paper introduces five notions, including π-algebras, π-ideals, Hopf π-algebras, π-modules and Hopf π-modules, verifies the fundamental isomorphism theorem of π-algebras and studies some algebraic properties of Hopf π-algebras as well.
1,322 citations
TL;DR: In this paper, the relation between the Hopf algebra associated to the renormalization of QFT and Hopf algebras associated to NCG computations of tranverse index theory for foliations is explored.
Abstract: We explore the relation between the Hopf algebra associated to the renormalization of QFT and the Hopf algebra associated to the NCG computations of tranverse index theory for foliations.
923 citations