# 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:

- FaMAF-CIEM (CONICET), Universidad Nacional de Córdoba Medina Allende s/n, Ciudad Universitaria (5000) Córdoba (Argentina)
- 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}

}

DOI: 10.1063/1.4907379

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