تقرير
Braid groups of imprimitive complex reflection groups
| العنوان: | Braid groups of imprimitive complex reflection groups |
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| المؤلفون: | Corran, Ruth, Lee, Eon-Kyung, Lee, Sang-Jin |
| المصدر: | Journal of Algebra 427 (2015) 387-425 |
| سنة النشر: | 2014 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Group Theory, Primary 20F55, 20F36, Secondary 20F05, 20F10, 03G10 |
| الوصف: | We obtain new presentations for the imprimitive complex reflection groups of type $(de,e,r)$ and their braid groups $B(de,e,r)$ for $d,r \ge 2$. Diagrams for these presentations are proposed. The presentations have much in common with Coxeter presentations of real reflection groups. They are positive and homogeneous, and give rise to quasi-Garside structures. Diagram automorphisms correspond to group automorphisms. The new presentation shows how the braid group $B(de,e,r)$ is a semidirect product of the braid group of affine type $\widetilde A_{r-1}$ and an infinite cyclic group. Elements of $B(de,e,r)$ are visualized as geometric braids on $r+1$ strings whose first string is pure and whose winding number is a multiple of $e$. We classify periodic elements, and show that the roots are unique up to conjugacy and that the braid group $B(de,e,r)$ is strongly translation discrete. Comment: published version |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1016/j.jalgebra.2015.01.004 |
| URL الوصول: | http://arxiv.org/abs/1404.5430 |
| رقم الأكسشن: | edsarx.1404.5430 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1016/j.jalgebra.2015.01.004 |
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