Characterisation and applications of k-split bimodules
| Autor: | Vanessa Miemietz, Xiaoting Zhang, Volodymyr Mazorchuk |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
General Mathematics Structure (category theory) 01 natural sciences Simple (abstract algebra) Mathematics::K-Theory and Homology Tensor (intrinsic definition) Mathematics::Quantum Algebra Mathematics::Category Theory FOS: Mathematics Projective module Representation Theory (math.RT) 0101 mathematics Algebra over a field Mathematics Discrete mathematics Transitive relation Functor Mathematics::Commutative Algebra Mathematics::Operator Algebras 010102 general mathematics Mathematics::Rings and Algebras Mathematics - Rings and Algebras Rings and Algebras (math.RA) Bimodule Mathematics - Representation Theory |
| Popis: | We describe the structure of bimodules (over finite dimensional algebras) which have the property that the functor of tensoring with such a bimodule sends any module to a projective module. The main result is that all such bimodules are $\Bbbk $-split in the sense that they factor (inside the tensor category of bimodules) over $\Bbbk $-vector spaces. As one application, we show that any simple $2$-category has a faithful $2$-representation inside the $2$-category of $\Bbbk $-split bimodules. As another application, we classify simple transitive $2$-representations of the $2$-category of projective bimodules over the algebra $\Bbbk [x,y]/(x^2,y^2,xy)$. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|