Open AccessBook
A guide to quantum groups
Vyjayanthi Chari,Andrew Pressley +1 more
TLDR
In this paper, the Kac-Moody algebras and quasitriangular Hopf algesas were used to represent the universal R-matrix and the root of unity case.Abstract:
Introduction 1. Poisson-Lie groups and Lie bialgebras 2. Coboundary Poisson-Lie groups and the classical Yang-Baxter equation 3. Solutions of the classical Yang-Baxter equation 4. Quasitriangular Hopf algebras 5. Representations and quasitensor categories 6. Quantization of Lie bialgebras 7. Quantized function algebras 8. Structure of QUE algebras: the universal R-matrix 9. Specializations of QUE algebras 10. Representations of QUE algebras: the generic case 11. Representations of QUE algebras: the root of unity case 12. Infinite-dimensional quantum groups 13. Quantum harmonic analysis 14. Canonical bases 15. Quantum group invariants of knots and 3-manifolds 16. Quasi-Hopf algebras and the Knizhnik-Zamolodchikov equation Appendix. The Kac-Moody algebras.read more
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On a Lorentz-invariant interpretation of noncommutative space-time and its implications on noncommutative QFT
TL;DR: By invoking the twisted Poincare symmetry of the algebra of functions on a Minkowski space-time, this paper showed that the non-commutative space time with the commutation relations [ x μ, x ν ] = i θ μ ν, where θμ ν is a constant real antisymmetric matrix, can be interpreted in a Lorentz-invariant way.
Journal ArticleDOI
The AdS 5 ×S 5 superstring worldsheet S matrix and crossing symmetry
TL;DR: An algebraic way to implement crossing relations for the AdS{sub 5}xS{sup 5} superstring worldsheet S matrix is proposed and generalized rapidities living on the universal cover of the parameter space which is constructed through an auxillary, coupling-constant dependent, elliptic curve.
Book
Noncommutative Geometry, Quantum Fields and Motives
Alain Connes,Matilde Marcolli +1 more
TL;DR: In this article, the Riemann zeta function and non-commutative spaces are studied in the context of quantum statistical mechanics and Galois symmetries, including the Weil explicit formula.
Book
Geometric Models for Noncommutative Algebras
TL;DR: The Poincare-Birkhoff-Witt theorem as discussed by the authors describes a Poisson geometry for algebraic deformation theory, which is a generalization of Weyl algebras.
Journal ArticleDOI
A gravity theory on noncommutative spaces
Paolo Aschieri,Christian Blohmann,Christian Blohmann,Marija Dimitrijevic,Marija Dimitrijevic,Marija Dimitrijevic,Frank Meyer,Frank Meyer,Peter Schupp,Julius Wess,Julius Wess +10 more
TL;DR: In this article, a deformation of the algebra of diffeomorphisms is constructed for canonically deformed spaces with constant deformation parameter?, and a covariant tensor calculus is constructed based on this deformed algebra, which can be interpreted as a?-deformed Einstein?Hilbert action.