Determinant and rank functions in semisimple pivotal Ab-categories | ||
| Categories and General Algebraic Structures with Applications | ||
| مقاله 4، دوره 19، شماره 1، آبان 2023، صفحه 47-80 اصل مقاله (620.32 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.48308/cgasa.19.1.47 | ||
| نویسندگان | ||
| Khalid Draoui* ؛ Hanan Choulli؛ Hakima Mouanis | ||
| Mathematical Sciences and Applications Laboratory, Department of Mathematics, Faculty of Sciences Dhar Al Mahraz, P. O. Box 1796, University Sidi Mohamed Ben Abdellah Fez, Morocco. | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Monoidal category؛ strong tensor functor؛ quantum trace؛ McCoy rank؛ quantum determinants | ||
| مراجع | ||
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