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- Title
Determinant and rank functions in semisimple pivotal Ab-categories.
- Authors
Draoui, Khalid; Choulli, Hanan; Mouanis, Hakima
- Abstract
We investigate and generalize quantum determinants to semisimple spherical and pivotal categories. It is well known that traces are preserved by strong tensor functors; we show on one hand that in fact, weaker conditions on a functor are sufficient to continue preserving traces. On the other hand, we prove that these determinants are well-behaved under strong tensor functors. Further, we introduce a notion of domination rank for objects of a semisimple pivotal category and prove similar properties of the ordinary case. Furthermore, we expand the determinantal and McCoy ranks to introduce a morphism quantum rank function on a semisimple pivotal category.
- Subjects
DETERMINANTAL varieties; ALGEBRA; MONOIDS; MORPHISMS (Mathematics); TENSOR algebra
- Publication
Categories & General Algebraic Structures with Applications, 2023, Vol 19, Issue 1, p47
- ISSN
2345-5853
- Publication type
Article
- DOI
10.48308/cgasa.19.1.47