Abstract
We provide a far reaching derived equivalence classification of the cluster-tilted algebras of Dynkin type D and suggest standard forms for the derived equivalence classes. We believe that the classification is complete, but some subtle questions remain open. We introduce another notion of equivalence called good mutation equivalence which is slightly stronger than derived equivalence but is algorithmically more tractable, and give a complete classification together with standard forms.
Original language | American English |
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Pages (from-to) | 277-332 |
Number of pages | 56 |
Journal | Journal of Algebra |
Volume | 410 |
DOIs | |
State | Published - 15 Jul 2014 |
Externally published | Yes |
Keywords
- Cartan determinant
- Cartan matrix
- Cluster tilted algebra
- Cluster tilting object
- Derived category
- Derived equivalence
- Dynkin diagram
- Finite representation type
- Good mutation
- Quiver mutation
- Tilting complex
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory