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On the 2-linearity of the free group

Authors
  • Licata, Anthony M.
Type
Preprint
Publication Date
Jun 21, 2016
Submission Date
Jun 21, 2016
Identifiers
arXiv ID: 1606.06444
Source
arXiv
License
Yellow
External links

Abstract

We construct an action of the free group $F_n$ on the homotopy category of projective modules over a finite dimensional zigzag algebra. The main theorem in the paper is that this action is faithful. We describe the relationship between homotopy classes of paths in the punctured disc and complexes of projective zigzag modules and explore the connection between gradings on the zigzag algebra and monoids in $F_n$. We use this connection to give homological constructions of the standard and Bessis dual word length metrics on the free group.

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