TY - JOUR
T1 - Presentations of Braid Groups of Type A Arising from (m+2)-angulations of Regular Polygons
AU - Morigi, Davide
N1 - Publisher Copyright:
© The Author(s) 2024.
PY - 2024/4
Y1 - 2024/4
N2 - Coloured quiver mutation, introduced by Buan, A.B., Thomas, H (Adv. Math. 222(3), 971–995 2009), gives a combinatorial interpretation of tilting in higher cluster categories. In type A work of Baur, K., Marsh, B. (Trans. Am. Math. Soc. 360(11), 5789-5803 2008) shows that m-coloured quivers and m-coloured quiver mutations have a nice geometrical description, given in terms of (m+2)-angulations of a regular polygon, and rotations of an m-diagonal. In this paper, using such correspondence, we describe presentations of braid groups of type A arising from coloured quivers of mutation type A.
AB - Coloured quiver mutation, introduced by Buan, A.B., Thomas, H (Adv. Math. 222(3), 971–995 2009), gives a combinatorial interpretation of tilting in higher cluster categories. In type A work of Baur, K., Marsh, B. (Trans. Am. Math. Soc. 360(11), 5789-5803 2008) shows that m-coloured quivers and m-coloured quiver mutations have a nice geometrical description, given in terms of (m+2)-angulations of a regular polygon, and rotations of an m-diagonal. In this paper, using such correspondence, we describe presentations of braid groups of type A arising from coloured quivers of mutation type A.
KW - 13F60
KW - 20F36
KW - Braid groups
KW - Cluster categories
KW - Mutation
UR - http://www.scopus.com/inward/record.url?scp=85184163174&partnerID=8YFLogxK
U2 - 10.1007/s10468-024-10257-x
DO - 10.1007/s10468-024-10257-x
M3 - Journal article
AN - SCOPUS:85184163174
SN - 1386-923X
VL - 27
SP - 1237
EP - 1265
JO - Algebras and Representation Theory
JF - Algebras and Representation Theory
IS - 2
ER -