Generalized trace and modified dimension functions on ribbon categories.(English)Zbl 1248.18006
Authors’ abstract: In this paper, we use topological techniques to construct generalized trace and modified dimension functions on ideals in certain ribbon categories. Examples of such ribbon categories naturally arise in representation theory where the usual trace and dimension functions are zero, but these generalized trace and modified dimension functions are nonzero. Such examples include categories of finite-dimensional modules of certain Lie algebras and finite groups over a field of positive characteristic and categories of finite-dimensional modules of basic Lie superalgebras over the complex numbers. These modified dimensions can be interpreted categorically and are closely related to some basic notions from representation theory.
Reviewer: Ye Jiachen (Shanghai)
MSC:
| 18D10 | Monoidal, symmetric monoidal and braided categories (MSC2010) |
| 17B99 | Lie algebras and Lie superalgebras |
| 20C99 | Representation theory of groups |
Keywords:
modular representations;Lie algebras;Lie superalgebras;tensor category;quantum group;trace;dimension;ribbon categoriesCite
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