Academic Journal
Non-degenerate potentials on the quiver X7.
| Τίτλος: | Non-degenerate potentials on the quiver X7. |
|---|---|
| Συγγραφείς: | Ladkani, Sefi1 (AUTHOR) ladkani.math@gmail.com |
| Πηγή: | Journal of Algebra. Mar2025, Vol. 666, p94-148. 55p. |
| Θεματικοί όροι: | *C*-algebras, *Mutations (Algebra), *Algebra, *Logical prediction, *Families, *Cluster algebras |
| Περίληψη: | We develop a method to compute certain mutations of quivers with potentials and use this to construct an explicit family of non-degenerate potentials on the exceptional quiver X 7. We confirm a conjecture of Geiss-Labardini-Schröer by presenting a computer-assisted proof that over a ground field of characteristic 2, the Jacobian algebra of one member W 0 of this family is infinite-dimensional, whereas that of another member W 1 is finite-dimensional, implying that these potentials are not right equivalent. As a consequence, we draw some conclusions on the associated cluster categories, and in particular obtain a representation-theoretic proof that there are no reddening mutation sequences for the quiver X 7. We also show that when the characteristic of the ground field differs from 2, the Jacobian algebras of W 0 and W 1 are both finite-dimensional. Thus W 0 seems to be the first known non-degenerate potential with the property that the finite-dimensionality of its Jacobian algebra depends upon the ground field. [ABSTRACT FROM AUTHOR] |
| Βάση Δεδομένων: | Academic Search Index |
καταχωρήστε σχόλιο πρώτοι!