# Differential graded algebras for trivalent plane graphs and their representations

@inproceedings{Sackel2021DifferentialGA, title={Differential graded algebras for trivalent plane graphs and their representations}, author={Kevin Sackel}, year={2021} }

To any trivalent plane graph embedded in the sphere, Casals and Murphy associate a differential graded algebra (dg-algebra), in which the underlying graded algebra is free associative over a commutative ring. Our first result is the construction of a generalization of the Casals–Murphy dg-algebra to non-commutative coefficients, for which we prove various functoriality properties not previously verified in the commutative setting. Our second result is to prove that rank r representations of…

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