- journal article metadata
European Mathematical Society Publishing House
2017-08-25 23:45:01
L’Enseignement Mathématique
Enseign. Math.
LEM
0013-8584
2309-4672
General
10.4171/LEM
http://www.ems-ph.org/doi/10.4171/LEM
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© Fondation L’Enseignement Mathématique
62
2016
3
Determinants over graded-commutative algebras, a categorical viewpoint
Tiffany
Covolo
Université de Luxembourg, Luxembourg
Jean-Philippe
Michel
Université de Liège, Belgium
Graded-commutative algebras, equivalence of categories, trace, determinant, Berezinian
We investigate 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.
Linear and multilinear algebra; matrix theory
Associative rings and algebras
Nonassociative rings and algebras
Category theory; homological algebra
361
420
10.4171/LEM/62-3/4-2
http://www.ems-ph.org/doi/10.4171/LEM/62-3/4-2