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Determinants over graded-commutative algebras, a categorical viewpoint
COVOLO, Tiffany; Michel, Jean-Philippe
2016
 

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Keywords :
graded-commutative algebras; equivalence of categories; trace; determinant; Berezinian
Abstract :
[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.
Disciplines :
Mathematics
Author, co-author :
COVOLO, Tiffany ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Michel, Jean-Philippe;  Université de Liège - ULg
Language :
English
Title :
Determinants over graded-commutative algebras, a categorical viewpoint
Publication date :
March 2016
Version :
3-4
Number of pages :
361–420
Available on ORBilu :
since 07 May 2014

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