Academic Journal
Προβολή σε EDS

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]
Βάση Δεδομένων: Academic Search Index
FullText Text:
  Availability: 0
CustomLinks:
  – Url: https://www.doi.org/10.1016/j.jalgebra.2026.05.020?
    Name: ScienceDirect (all content) (s7799221)
    Category: fullText
    Text: View record from ScienceDirect
    MouseOverText: View record from ScienceDirect
  – Url: https://resolver.ebsco.com/c/fiv2js/result?sid=EBSCO:asx&genre=article&issn=00218693&ISBN=&volume=706&issue=&date=20261115&spage=79&pages=79-169&title=Journal of Algebra&atitle=H-based%20quivers%20with%20potentials%20and%20their%20representations.&aulast=Lin%2C%20Xiaoyue&id=DOI:10.1016/j.jalgebra.2026.05.020
    Name: Full Text Finder (for New FTF UI) (ns324271)
    Category: fullText
    Text: Full Text Finder
    MouseOverText: Full Text Finder
Header DbId: asx
DbLabel: Academic Search Index
An: 196057736
RelevancyScore: 1437
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 1436.685546875
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: H-based quivers with potentials and their representations.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Lin%2C+Xiaoyue%22">Lin, Xiaoyue</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> xiao_yue_lin@sjtu.edu.cn</i>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="JN" term="%22Journal+of+Algebra%22">Journal of Algebra</searchLink>. Nov2026, Vol. 706, p79-169. 91p.
– Name: Subject
  Label: Subject Terms
  Group: Su
  Data: *<searchLink fieldCode="DE" term="%22Mutations+%28Algebra%29%22">Mutations (Algebra)</searchLink><br />*<searchLink fieldCode="DE" term="%22Cluster+algebras%22">Cluster algebras</searchLink><br />*<searchLink fieldCode="DE" term="%22Polynomials%22">Polynomials</searchLink><br />*<searchLink fieldCode="DE" term="%22Ideals+%28Algebra%29%22">Ideals (Algebra)</searchLink><br />*<searchLink fieldCode="DE" term="%22Representation+theory%22">Representation theory</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: 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]
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=asx&AN=196057736
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1016/j.jalgebra.2026.05.020
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 91
        StartPage: 79
    Subjects:
      – SubjectFull: Mutations (Algebra)
        Type: general
      – SubjectFull: Cluster algebras
        Type: general
      – SubjectFull: Polynomials
        Type: general
      – SubjectFull: Ideals (Algebra)
        Type: general
      – SubjectFull: Representation theory
        Type: general
    Titles:
      – TitleFull: H-based quivers with potentials and their representations.
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Lin, Xiaoyue
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 15
              M: 11
              Text: Nov2026
              Type: published
              Y: 2026
          Identifiers:
            – Type: issn-print
              Value: 00218693
          Numbering:
            – Type: volume
              Value: 706
          Titles:
            – TitleFull: Journal of Algebra
              Type: main
ResultId 1