Research output: Contribution to journal › Journal article

Published

<mark>Journal publication date</mark> | 15/12/2007 |
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<mark>Journal</mark> | Journal of Algebra |

Issue number | 2 |

Volume | 318 |

Number of pages | 20 |

Pages (from-to) | 933-952 |

<mark>State</mark> | Published |

<mark>Original language</mark> | English |

Let k be an algebraically closed field of characteristic 2. We prove that the restricted nilpotent commuting variety C, that is the set of pairs of (n×n)-matrices (A,B) such that A2=B2=[A,B]=0, is equidimensional. C can be identified with the ‘variety of n-dimensional modules’ for Z/2Z×Z/2Z, or equivalently, for k[X,Y]/(X2,Y2). On the other hand, we provide an example showing that the restricted nilpotent commuting variety is not equidimensional for fields of characteristic >2. We also prove that if e2=0 then the set of elements of the centralizer of e whose square is zero is equidimensional. Finally, we express each irreducible component of C as a direct sum of indecomposable components of varieties of Z/2Z×Z/2Z-modules.