H-based quivers with potentials and their representations.

Λεπτομέρειες βιβλιογραφικής εγγραφής
Τίτλος:	H-based quivers with potentials and their representations.
Συγγραφείς:	Lin, Xiaoyue¹ (AUTHOR) xiao_yue_lin@sjtu.edu.cn
Πηγή:	Journal of Algebra. Nov2026, Vol. 706, p79-169. 91p.
Θεματικοί όροι:	Mutations (Algebra), Cluster algebras, Polynomials, Ideals (Algebra), *Representation theory
Περίληψη:	We generalize Derksen-Weyman-Zelevinsky's theory of quivers with potentials (QPs) to an H -based setting by considering quivers with exactly one loop at each vertex, asking the loops to be nilpotent and so attaching a truncated polynomial ring H i to each vertex. The algebra is then defined by taking the quotient of the complete path algebra by relations arising from analogs of the Jacobian ideals of a given potential. We develop the mutation theory for such H -based QPs and their decorated representations in general position. As an application, we consider generalized cluster algebras introduced by Chekhov-Shapiro. For those algebras corresponding to H -based quivers (Q , d) that have mutation degree d k ≤ 2 at each vertex k and admit nondegenerate potentials S making (Q , d , S) locally free, we provide a representation-theoretic interpretation of g -vectors and F -polynomials. We further construct generic character for upper generalized cluster algebras. [ABSTRACT FROM AUTHOR]
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