### Abstract

^{n}-families of solutions of the YangBaxter equation from nproducts of three-dimensional R and L operators satisfying the tetrahedron equation. They are identified with the quantum R matrices for the Hopf algebras known as generalized quantum groups. Depending on the number of 1's and L's involved in the product, the trace construction interpolates the symmetric tensor representations of Uq (An-1

^{(1)}) and the antisymmetric tensor representations of U-q

^{-1}(An-1

^{(1)}), whereas a boundary vector construction interpolates the q-oscillator representation of Uq (Dn 1) (2) + and the spin representation of Uq (Dn+1

^{(2)}) . The intermediate cases are associated with an affinization of quantum superalgebras.

Original language | English |
---|---|

Pages (from-to) | 1-29 |

Number of pages | 29 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 48 |

Issue number | 30 |

DOIs | |

Publication status | Published - 2015 |

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### Cite this

*Journal of Physics A: Mathematical and Theoretical*,

*48*(30), 1-29. https://doi.org/10.1088/1751-8113/48/30/304001

}

*Journal of Physics A: Mathematical and Theoretical*, vol. 48, no. 30, pp. 1-29. https://doi.org/10.1088/1751-8113/48/30/304001

**Tetrahedron equation and generalized quantum groups.** / Kuniba, Atsuo; Okado, M; Sergeev, Sergey.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Tetrahedron equation and generalized quantum groups

AU - Kuniba, Atsuo

AU - Okado, M

AU - Sergeev, Sergey

PY - 2015

Y1 - 2015

N2 - We construct 2n-families of solutions of the YangBaxter equation from nproducts of three-dimensional R and L operators satisfying the tetrahedron equation. They are identified with the quantum R matrices for the Hopf algebras known as generalized quantum groups. Depending on the number of 1's and L's involved in the product, the trace construction interpolates the symmetric tensor representations of Uq (An-1(1)) and the antisymmetric tensor representations of U-q-1 (An-1(1)), whereas a boundary vector construction interpolates the q-oscillator representation of Uq (Dn 1) (2) + and the spin representation of Uq (Dn+1(2)) . The intermediate cases are associated with an affinization of quantum superalgebras.

AB - We construct 2n-families of solutions of the YangBaxter equation from nproducts of three-dimensional R and L operators satisfying the tetrahedron equation. They are identified with the quantum R matrices for the Hopf algebras known as generalized quantum groups. Depending on the number of 1's and L's involved in the product, the trace construction interpolates the symmetric tensor representations of Uq (An-1(1)) and the antisymmetric tensor representations of U-q-1 (An-1(1)), whereas a boundary vector construction interpolates the q-oscillator representation of Uq (Dn 1) (2) + and the spin representation of Uq (Dn+1(2)) . The intermediate cases are associated with an affinization of quantum superalgebras.

KW - generalized quantum groups

KW - tetrahedron equation

KW - YangBaxter equation

UR - http://www.scopus.com/inward/record.url?scp=84937010940&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/tetrahedron-equation-generalized-quantum-groups

U2 - 10.1088/1751-8113/48/30/304001

DO - 10.1088/1751-8113/48/30/304001

M3 - Article

VL - 48

SP - 1

EP - 29

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

SN - 1751-8113

IS - 30

ER -