### Abstract

We compute the R-matrix which intertwines two-dimensional evaluation representations with Drinfeld comultiplication for U_{q} (sl_{2}). This R-matrix contains terms proportional to the δ-function. We construct the algebra A(R) generated by the elements of the matrices L^{±}(z) with relations determined by R using the formulation of Reshetikhin-Semenov-Tian-Shansky. In the category of highest-weight representations, there is a Hopf algebra isomorphism between A(R) and an extension Ū9(sl_{2}) of Drinfeld's algebra.

Original language | English (US) |
---|---|

Pages (from-to) | 149-160 |

Number of pages | 12 |

Journal | Letters in Mathematical Physics |

Volume | 41 |

Issue number | 2 |

DOIs | |

State | Published - Jul 2 1997 |

Externally published | Yes |

### Fingerprint

### Keywords

- Drinfeld comultiplication
- Hopf algebra
- R-matrices

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

**Singular R-Matrices and Drinfeld's Comultiplication.** / Kedem, Rinat.

Research output: Contribution to journal › Article

*Letters in Mathematical Physics*, vol. 41, no. 2, pp. 149-160. https://doi.org/10.1023/A:1007373719529

}

TY - JOUR

T1 - Singular R-Matrices and Drinfeld's Comultiplication

AU - Kedem, Rinat

PY - 1997/7/2

Y1 - 1997/7/2

N2 - We compute the R-matrix which intertwines two-dimensional evaluation representations with Drinfeld comultiplication for Uq (sl2). This R-matrix contains terms proportional to the δ-function. We construct the algebra A(R) generated by the elements of the matrices L±(z) with relations determined by R using the formulation of Reshetikhin-Semenov-Tian-Shansky. In the category of highest-weight representations, there is a Hopf algebra isomorphism between A(R) and an extension Ū9(sl2) of Drinfeld's algebra.

AB - We compute the R-matrix which intertwines two-dimensional evaluation representations with Drinfeld comultiplication for Uq (sl2). This R-matrix contains terms proportional to the δ-function. We construct the algebra A(R) generated by the elements of the matrices L±(z) with relations determined by R using the formulation of Reshetikhin-Semenov-Tian-Shansky. In the category of highest-weight representations, there is a Hopf algebra isomorphism between A(R) and an extension Ū9(sl2) of Drinfeld's algebra.

KW - Drinfeld comultiplication

KW - Hopf algebra

KW - R-matrices

UR - http://www.scopus.com/inward/record.url?scp=1842789881&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1842789881&partnerID=8YFLogxK

U2 - 10.1023/A:1007373719529

DO - 10.1023/A:1007373719529

M3 - Article

AN - SCOPUS:1842789881

VL - 41

SP - 149

EP - 160

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

SN - 0377-9017

IS - 2

ER -