30 citations · 103 across the 9 of their papers we have counts for
10 papers
Local Forms of Morphisms of Colored Supermanifolds
Tiffany Covolo, Stephen Kwok, Norbert Poncin
In \cite{Covolo:2016}, \cite{Covolo:2012} and \cite{Poncin:2016}, we introduced the category of colored supermanifolds (-super\-ma\-ni\-folds or just $\mathbb{Z}_2^…
The Frobenius theorem for -supermanifolds
Tiffany Covolo, Stephen Kwok, Norbert Poncin
We continue the development of -supergeometry, a natural generalization of classical (-graded) supergeometry, by proving the Frobenius theorem for int…
Differential calculus on -supermanifolds
Tiffany Covolo, Stephen Kwok, Norbert Poncin
The concept of $\Zn$-supermanifold has been recently proposed as a natural generalization of classical ($\Zs$-graded) supergeometry, allowing for more complicated commutativity con…
Splitting theorem for -supermanifolds
Tiffany Covolo, Janusz Grabowski, Norbert Poncin
Smooth -supermanifolds have been introduced and studied recently. The corresponding sign rule is given by the "scalar product" of the involved -degr…
The category of -supermanifolds
Tiffany Covolo, Janusz Grabowski, Norbert Poncin
In Physics and in Mathematics -gradings, , appear in various fields. The corresponding sign rule is determined by the `scalar product' of the involved $\mathbb…
-Supergeometry II: Batchelor-Gawedzki Theorem
Tiffany Covolo, Janusz Grabowski, Norbert Poncin
Quite a number of -gradings, , appear in Physics and in Mathematics. The corresponding sign rules are given by the `scalar product' of the involved $\mathb…
-Supergeometry I: Manifolds and Morphisms
Tiffany Covolo, Janusz Grabowski, Norbert Poncin
In Physics and in Mathematics -gradings, , do appear quite frequently. The corresponding sign rules are determined by the `scalar product' of the involved…
Determinants over graded-commutative algebras, a categorical viewpoint
Tiffany Covolo, Jean-Philippe Michel
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 cate…
Cohomological Approach to the Graded Berezinian
Tiffany Covolo
We develop the theory of linear algebra over a (Z_2)^n-commutative algebra (n in N), which includes the well-known super linear algebra as a special case (n=1). Examples of such gr…
Higher Trace and Berezinian of Matrices over a Clifford Algebra
Tiffany Covolo, Valentin Ovsienko, Norbert Poncin
We define the notions of trace, determinant and, more generally, Berezinian of matrices over a (Z_2)^n graded commutative associative algebra. The applications include a new approa…