Academic Journal
On the irreducibility of the extension of the Lawrence–Bigelow–Krammer representation to the virtual braid group VB3.
| Τίτλος: | On the irreducibility of the extension of the Lawrence–Bigelow–Krammer representation to the virtual braid group VB3. |
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| 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 |
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