Academic Journal
Προβολή σε EDS

On the irreducibility of the extension of the Lawrence–Bigelow–Krammer representation to the virtual braid group VB3.

Λεπτομέρειες βιβλιογραφικής εγγραφής
Τίτλος: On the irreducibility of the extension of the Lawrence–Bigelow–Krammer representation to the virtual braid group VB3.
Συγγραφείς: Chreif, Mohamad Y.1 (AUTHOR) mohamad.chreif@liu.edu.lb, Dally, Malak M.2 (AUTHOR) m.dalla@bau.edu.lb
Πηγή: Journal of Knot Theory & Its Ramifications. Sep2026, p1. 11p.
Θεματικοί όροι: *Braid group (Knot theory), *Representations of groups (Algebra), *Complex variables, *Representation theory
Περίληψη: In this paper, we consider the representation Ψ : VB3 →GL3(ℤ[t±t,t 1±t,t 2±t]) which extends the Lawrence–Bigelow–Krammer representation from the braid group B3 to the virtual braid group VB3 on three strands. After specializing parameters t,t1, t2 to non-zero complex numbers, we study the irreducibility of Ψ. We prove that Ψ is irreducible for all non-zero complex numbers t,t1, t2 except for the case t = t1 = t2 ∈{1,−1}. [ABSTRACT FROM AUTHOR]
Βάση Δεδομένων: Academic Search Index
FullText Text:
  Availability: 0
Header DbId: asx
DbLabel: Academic Search Index
An: 197241330
RelevancyScore: 1452
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 1452.42810058594
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: On the irreducibility of the extension of the Lawrence–Bigelow–Krammer representation to the virtual braid group VB3.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Chreif%2C+Mohamad+Y%2E%22">Chreif, Mohamad Y.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> mohamad.chreif@liu.edu.lb</i><br /><searchLink fieldCode="AR" term="%22Dally%2C+Malak+M%2E%22">Dally, Malak M.</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> m.dalla@bau.edu.lb</i>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="JN" term="%22Journal+of+Knot+Theory+%26+Its+Ramifications%22">Journal of Knot Theory & Its Ramifications</searchLink>. Sep2026, p1. 11p.
– Name: Subject
  Label: Subject Terms
  Group: Su
  Data: *<searchLink fieldCode="DE" term="%22Braid+group+%28Knot+theory%29%22">Braid group (Knot theory)</searchLink><br />*<searchLink fieldCode="DE" term="%22Representations+of+groups+%28Algebra%29%22">Representations of groups (Algebra)</searchLink><br />*<searchLink fieldCode="DE" term="%22Complex+variables%22">Complex variables</searchLink><br />*<searchLink fieldCode="DE" term="%22Representation+theory%22">Representation theory</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: In this paper, we consider the representation Ψ : VB3 →GL3(ℤ[t±t,t 1±t,t 2±t]) which extends the Lawrence–Bigelow–Krammer representation from the braid group B3 to the virtual braid group VB3 on three strands. After specializing parameters t,t1, t2 to non-zero complex numbers, we study the irreducibility of Ψ. We prove that Ψ is irreducible for all non-zero complex numbers t,t1, t2 except for the case t = t1 = t2 ∈{1,−1}. [ABSTRACT FROM AUTHOR]
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=asx&AN=197241330
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1142/s0218216526500562
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 11
        StartPage: 1
    Subjects:
      – SubjectFull: Braid group (Knot theory)
        Type: general
      – SubjectFull: Representations of groups (Algebra)
        Type: general
      – SubjectFull: Complex variables
        Type: general
      – SubjectFull: Representation theory
        Type: general
    Titles:
      – TitleFull: On the irreducibility of the extension of the Lawrence–Bigelow–Krammer representation to the virtual braid group VB3.
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Chreif, Mohamad Y.
      – PersonEntity:
          Name:
            NameFull: Dally, Malak M.
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 23
              M: 09
              Text: Sep2026
              Type: published
              Y: 2026
          Identifiers:
            – Type: issn-print
              Value: 02182165
          Titles:
            – TitleFull: Journal of Knot Theory & Its Ramifications
              Type: main
ResultId 1