Topic
Quantum group
About: Quantum group is a research topic. Over the lifetime, 7551 publications have been published within this topic receiving 206662 citations.
Papers published on a yearly basis
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Papers
Book•
1 Jan 1983TL;DR: The invariant bilinear form and the generalized casimir operator are integral representations of Kac-Moody algebras and the weyl group as mentioned in this paper, as well as a classification of generalized cartan matrices.
Abstract: Introduction Notational conventions 1 Basic definitions 2 The invariant bilinear form and the generalized casimir operator 3 Integrable representations of Kac-Moody algebras and the weyl group 4 A classification of generalized cartan matrices 5 Real and imaginary roots 6 Affine algebras: the normalized cartan invariant form, the root system, and the weyl group 7 Affine algebras as central extensions of loop algebras 8 Twisted affine algebras and finite order automorphisms 9 Highest-weight modules over Kac-Moody algebras 10 Integrable highest-weight modules: the character formula 11 Integrable highest-weight modules: the weight system and the unitarizability 12 Integrable highest-weight modules over affine algebras 13 Affine algebras, theta functions, and modular forms 14 The principal and homogeneous vertex operator constructions of the basic representation Index of notations and definitions References Conference proceedings and collections of paper
5,902 citations
Book•
1 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.
3,046 citations
Book•
1 Jan 1962
TL;DR: In this paper, the authors present a group theory representation and modular representation for algebraic number theory, including Semi-Semi-Simple Rings and Group Algebras, including Frobenius Algebraic numbers.
Abstract: Notation Background from Group Theory Representations and Modules Algebraic Number Theory Semi-Simple Rings and Group Algebras Group Characters Induced Characters Induced Representation Non-Semi-Simple Rings Frobenius Algebras Splitting Fields and Separable Algebras Integral Representations Modular Representations Index
2,906 citations
Book•
1 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.
2,628 citations
TL;DR: In this article, a new class of commutative algebras was proposed for dual canonical bases and total positivity in semisimple groups. But the study of the algebraic framework is not yet complete.
Abstract: In an attempt to create an algebraic framework for dual canonical bases and total positivity in semisimple groups, we initiate the study of a new class of commutative algebras.
2,284 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 9 |
| 2024 | 18 |
| 2023 | 52 |
| 2022 | 131 |
| 2021 | 85 |
| 2020 | 91 |