Finite-Dimensional Representations Of Leavitt Path Algebras
| Autor: | Ayten Koç, Murad Özaydin |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Path (topology)
Pure mathematics Reduction (recursion theory) quiver representations General Mathematics Astrophysics::High Energy Astrophysical Phenomena Leavitt path algebra nonstable K-theory 01 natural sciences Graph Mathematics::Category Theory 0103 physical sciences Almost surely 0101 mathematics Morita equivalence Mathematics::Representation Theory Mathematics graph monoid Subcategory Applied Mathematics 010102 general mathematics Quiver Mathematics::Rings and Algebras Dimension function Digraph finite-dimensional modules dimension function K-Theory 010307 mathematical physics |
| Popis: | When Γ is a row-finite digraph, we classify all finite-dimensional modules of the Leavitt path algebra L ( Γ ) {L(\Gamma)} via an explicit Morita equivalence given by an effective combinatorial (reduction) algorithm on the digraph Γ. The category of (unital) L ( Γ ) {L(\Gamma)} -modules is equivalent to a full subcategory of quiver representations of Γ. However, the category of finite-dimensional representations of L ( Γ ) {L(\Gamma)} is tame in contrast to the finite-dimensional quiver representations of Γ, which are almost always wild. |
| Databáze: | OpenAIRE |
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