## Abstract

We study the generalized Clifford algebras associated to homogeneous binary forms of prime degree p, focusing on exponentiation forms of p-central spaces in division algebra. For a two-dimensional p-central space, we make the simplifying assumption that one basis element is a sum of two eigenvectors with respect to conjugation by the other. If the product of the eigenvalues is 1 then the Clifford algebra is a symbol Azumaya algebra of degree p, generalizing the theory developed for p= 3. Furthermore, when p= 5 and the product is not 1, we show that any quotient division algebra of the Clifford algebra is a cyclic algebra or a tensor product of two cyclic algebras, and every product of two cyclic algebras can be obtained as a quotient. Explicit presentation is given to the Clifford algebra when the form is diagonal.

Original language | English |
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Pages (from-to) | 94-111 |

Number of pages | 18 |

Journal | Journal of Algebra |

Volume | 366 |

DOIs | |

State | Published - 15 Sep 2012 |

### Bibliographical note

Funding Information:✩ This research was supported by the Binational US–Israel Science Foundation, grant # 2010/149.

### Funding

✩ This research was supported by the Binational US–Israel Science Foundation, grant # 2010/149.

Funders | Funder number |
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United States-Israel Binational Science Foundation | 2010/149 |

## Keywords

- Cyclic algebra
- Eigenvector decomposition
- Generalized Clifford algebra
- P-Central space
- Primary
- Secondary