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Title: CLUSTER ALGEBRAS FROM SURFACES AND EXTENDED AFFINE WEYL GROUPS
We characterize mutation-finite cluster algebras of rank at least 3 using positive semi-definite quadratic forms. In particular, we associate with every unpunctured bordered surface a positive semi-definite quadratic space V , and with every triangulation a basis in V , such that any mutation of a cluster (i.e., a flip of a triangulation) transforms the corresponding bases into each other by partial reflections. Furthermore, every triangulation gives rise to an extended affine Weyl group of type A, which is invariant under flips. The construction is also extended to exceptional skew-symmetric mutation-finite cluster algebras of types E.  more » « less
Award ID(s):
1702115
PAR ID:
10345565
Author(s) / Creator(s):
; ; ;
Date Published:
Journal Name:
Transformation groups
Volume:
26
Issue:
2
ISSN:
1083-4362
Page Range / eLocation ID:
501–535
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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