Λεπτομέρειες βιβλιογραφικής εγγραφής
| 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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