Reference : Higher trace and Berezinian of matrices over a Clifford algebra |

Scientific journals : Article | |||

Physical, chemical, mathematical & earth Sciences : Mathematics | |||

http://hdl.handle.net/10993/9369 | |||

Higher trace and Berezinian of matrices over a Clifford algebra | |

English | |

Covolo, Tiffany [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >] | |

Ovsienko, Valentin [CNRS, Institut Camille Jordan, Université Claude Bernard Lyon 1] | |

Poncin, Norbert [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >] | |

2012 | |

Journal of Geometry and Physics | |

Elsevier | |

62 | |

11 | |

2294–2319 | |

Yes (verified by ORBi^{lu}) | |

International | |

0393-0440 | |

[en] We define the notions of trace, determinant and, more generally, Berezinian of matrices
over a (Z_2)^n-graded commutative associative algebra A. The applications include a new approach to the classical theory of matrices with coefficients in a Clifford algebra, in particular of quaternionic matrices. In a special case, we recover the classical Dieudonné determinant of quaternionic matrices, but in general our quaternionic determinant is different. We show that the graded determinant of purely even (Z_2)^n-graded matrices of degree 0 is polynomial in its entries. In the case of the algebra A = H of quaternions, we calculate the formula for the Berezinian in terms of a product of quasiminors in the sense of Gelfand, Retakh, and Wilson. The graded trace is related to the graded Berezinian (and determinant) by a (Z_2)^n-graded version of Liouville’s formula. | |

http://hdl.handle.net/10993/9369 | |

10.1016/j.geomphys.2012.07.004 | |

http://www.sciencedirect.com.proxy.bnl.lu/science/article/pii/S0393044012001386 | |

http://arxiv.org/abs/1109.5877 |

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