Reference : Determinants over graded-commutative algebras, a categorical viewpoint
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Physical, chemical, mathematical & earth Sciences : Mathematics
Determinants over graded-commutative algebras, a categorical viewpoint
Covolo, Tiffany [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Michel, Jean-Philippe mailto [Université de Liège - ULg]
L'Enseignement Mathématique 62
[en] graded-commutative algebras ; equivalence of categories ; trace ; determinant ; Berezinian
[en] We generalize linear superalgebra to higher gradings and commutation factors, given by arbitrary abelian groups and bicharacters. Our central tool is an extension, to monoidal categories of modules, of the Nekludova-Scheunert faithful functor between the categories of graded-commutative and supercommutative algebras. As a result we generalize (super-)trace, determinant and Berezinian to graded matrices over graded-commutative algebras. For instance, on homogeneous quaternionic matrices, we obtain a lift of the Dieudonné determinant to the skew-field of quaternions.

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