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## Abstract

Assume that F is an algebraically closed field with characteristic zero. The Racah algebra ℜ is the unital associative F-algebra defined by generators and relations in the following way. The generators are A, B, C, D and the relations assert that [A, B] = [B, C] = [C, A] = 2D and that each of [A, D]+AC−BA, [B, D]+BA−CB, [C, D]+CB−AC is central in ℜ. In this paper we discuss the finite-dimensional irreducible R-modules in detail and classify them up to isomorphism. To do this, we apply an infinite-dimensional R-module and its universal property. We additionally give the necessary and sufficient conditions for A, B, C to be diagonalizable on finite-dimensional irreducible R-modules.

Original language | English |
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Article number | 018 |

Journal | Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) |

Volume | 16 |

DOIs | |

State | Published - 2020 |

## Keywords

- Irreducible modules
- Quadratic algebra
- Racah algebra
- Tridiagonal pairs
- Universal property

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Dive into the research topics of 'Finite-dimensional irreducible modules of the racah algebra at characteristic zero'. Together they form a unique fingerprint.## Projects

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