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On the composition of the Cohen map and the Tong–Yang–Ma representation.

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Τίτλος: On the composition of the Cohen map and the Tong–Yang–Ma representation.
Συγγραφείς: Moulla, Amal F.1 (AUTHOR) afm455@student.bau.edu.lb, Abdulrahim, Mohammad N.1 (AUTHOR) mna@bau.edu.lb
Πηγή: Arabian Journal of Mathematics. Jun2026, p1-7. 7p.
Θεματικοί όροι: *Braid group (Knot theory), *Representations of groups (Algebra), *Transformation groups, *Linear algebra, *Algebraic topology, *Homomorphisms
Περίληψη: We study the composition of F. R. Cohen map Bn→Bnk\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$B_n\rightarrow B_{n k}$$\end{document} with the Tong-Yang-Ma representation Bnk→GLnk(Z[t±1])\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$B_{nk}\rightarrow GL_{nk}(\mathbb {Z}[t^{\pm 1}])$$\end{document} in the case k=2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$k=2$$\end{document}, where Bn\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$B_n$$\end{document} is the braid group on n strings. We prove that the transpose of the representation thus obtained of degree 2n is the direct sum of two copies of Tong-Yang-Ma representations, each of degree n, with t replaced by t2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$t^2$$\end{document}. [ABSTRACT FROM AUTHOR]
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  – Url: https://resolver.ebsco.com/c/fiv2js/result?sid=EBSCO:asx&genre=article&issn=21935343&ISBN=&volume=&issue=&date=20260608&spage=1&pages=1-7&title=Arabian Journal of Mathematics&atitle=On%20the%20composition%20of%20the%20Cohen%20map%20and%20the%20Tong%E2%80%93Yang%E2%80%93Ma%20representation.&aulast=Moulla%2C%20Amal%20F.&id=DOI:10.1007/s40065-026-00653-0
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Items – Name: Title
  Label: Title
  Group: Ti
  Data: On the composition of the Cohen map and the Tong–Yang–Ma representation.
– Name: Author
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  Data: <searchLink fieldCode="AR" term="%22Moulla%2C+Amal+F%2E%22">Moulla, Amal F.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> afm455@student.bau.edu.lb</i><br /><searchLink fieldCode="AR" term="%22Abdulrahim%2C+Mohammad+N%2E%22">Abdulrahim, Mohammad N.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> mna@bau.edu.lb</i>
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  Label: Source
  Group: Src
  Data: <searchLink fieldCode="JN" term="%22Arabian+Journal+of+Mathematics%22">Arabian Journal of Mathematics</searchLink>. Jun2026, p1-7. 7p.
– Name: Subject
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  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="%22Transformation+groups%22">Transformation groups</searchLink><br />*<searchLink fieldCode="DE" term="%22Linear+algebra%22">Linear algebra</searchLink><br />*<searchLink fieldCode="DE" term="%22Algebraic+topology%22">Algebraic topology</searchLink><br />*<searchLink fieldCode="DE" term="%22Homomorphisms%22">Homomorphisms</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: We study the composition of F. R. Cohen map Bn→Bnk\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$B_n\rightarrow B_{n k}$$\end{document} with the Tong-Yang-Ma representation Bnk→GLnk(Z[t±1])\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$B_{nk}\rightarrow GL_{nk}(\mathbb {Z}[t^{\pm 1}])$$\end{document} in the case k=2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$k=2$$\end{document}, where Bn\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$B_n$$\end{document} is the braid group on <italic>n</italic> strings. We prove that the transpose of the representation thus obtained of degree 2<italic>n</italic> is the direct sum of two copies of Tong-Yang-Ma representations, each of degree <italic>n</italic>, with <italic>t</italic> replaced by t2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$t^2$$\end{document}. [ABSTRACT FROM AUTHOR]
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RecordInfo BibRecord:
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    Identifiers:
      – Type: doi
        Value: 10.1007/s40065-026-00653-0
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 7
        StartPage: 1
    Subjects:
      – SubjectFull: Braid group (Knot theory)
        Type: general
      – SubjectFull: Representations of groups (Algebra)
        Type: general
      – SubjectFull: Transformation groups
        Type: general
      – SubjectFull: Linear algebra
        Type: general
      – SubjectFull: Algebraic topology
        Type: general
      – SubjectFull: Homomorphisms
        Type: general
    Titles:
      – TitleFull: On the composition of the Cohen map and the Tong–Yang–Ma representation.
        Type: main
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            NameFull: Moulla, Amal F.
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          Name:
            NameFull: Abdulrahim, Mohammad N.
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          Dates:
            – D: 08
              M: 06
              Text: Jun2026
              Type: published
              Y: 2026
          Identifiers:
            – Type: issn-print
              Value: 21935343
          Titles:
            – TitleFull: Arabian Journal of Mathematics
              Type: main
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