### Abstract

A differential central simple algebra, and in particular a differential matrix algebra, over a differential field K with constants C can be trivialized by a Picard-Vessiot (differential Galois) extension E.In the matrix algebra case, there is a correspondence between K-algebras trivialized by E and representations of the Galois group of E over K in PGL_{n}(C), which can be interpreted as cocyles equivalent up to coboundaries.

Original language | English |
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Pages (from-to) | 1911-1918 |

Number of pages | 8 |

Journal | Proceedings of the American Mathematical Society |

Volume | 136 |

Issue number | 6 |

DOIs | |

State | Published - Jun 2008 |

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## Cite this

Juan, L., & Magid, A. R. (2008). Differential central simple algebras and picard-vessiot representations.

*Proceedings of the American Mathematical Society*,*136*(6), 1911-1918. https://doi.org/10.1090/S0002-9939-08-09165-X