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Title: The R-matrix of quantum doubles of Nichols algebras of diagonal type

Abstract

Let H be the quantum double of a Nichols algebra of diagonal type. We compute the R-matrix of 3-tuples of modules for general finite-dimensional highest weight modules over H. We also calculate a multiplicative formula for the universal R-matrix when H is finite dimensional. We show the unicity of a PBW basis (or a Lusztig-type Poincaré-Birkhoff-Witt basis) with a given convex order.

Authors:
 [1];  [2]
  1. FaMAF-CIEM (CONICET), Universidad Nacional de Córdoba Medina Allende s/n, Ciudad Universitaria (5000) Córdoba (Argentina)
  2. University of Toyama, Faculty of Science, Gofuku 3190, Toyama-shi, Toyama 930-8555 (Japan)
Publication Date:
OSTI Identifier:
22403094
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 2; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; GROUP THEORY; QUANTUM GROUPS; R MATRIX; WEIGHT

Citation Formats

Angiono, Iván, E-mail: angiono@famaf.unc.edu.ar, and Yamane, Hiroyuki, E-mail: hiroyuki@sci.u-toyama.ac.jp. The R-matrix of quantum doubles of Nichols algebras of diagonal type. United States: N. p., 2015. Web. doi:10.1063/1.4907379.
Angiono, Iván, E-mail: angiono@famaf.unc.edu.ar, & Yamane, Hiroyuki, E-mail: hiroyuki@sci.u-toyama.ac.jp. The R-matrix of quantum doubles of Nichols algebras of diagonal type. United States. doi:10.1063/1.4907379.
Angiono, Iván, E-mail: angiono@famaf.unc.edu.ar, and Yamane, Hiroyuki, E-mail: hiroyuki@sci.u-toyama.ac.jp. Sun . "The R-matrix of quantum doubles of Nichols algebras of diagonal type". United States. doi:10.1063/1.4907379.
@article{osti_22403094,
title = {The R-matrix of quantum doubles of Nichols algebras of diagonal type},
author = {Angiono, Iván, E-mail: angiono@famaf.unc.edu.ar and Yamane, Hiroyuki, E-mail: hiroyuki@sci.u-toyama.ac.jp},
abstractNote = {Let H be the quantum double of a Nichols algebra of diagonal type. We compute the R-matrix of 3-tuples of modules for general finite-dimensional highest weight modules over H. We also calculate a multiplicative formula for the universal R-matrix when H is finite dimensional. We show the unicity of a PBW basis (or a Lusztig-type Poincaré-Birkhoff-Witt basis) with a given convex order.},
doi = {10.1063/1.4907379},
journal = {Journal of Mathematical Physics},
number = 2,
volume = 56,
place = {United States},
year = {Sun Feb 15 00:00:00 EST 2015},
month = {Sun Feb 15 00:00:00 EST 2015}
}