Abstract
In this note, we initiate a study of the finite-dimensional representation theory of a class of algebras that correspond to noncommutative deformations of compact surfaces of arbitrary genus. Low dimensional representations are investigated in detail and graph representations are used in order to understand the structure of non-zero matrix elements. In particular, for arbitrary genus greater than one, we explicitly construct classes of irreducible two and three dimensional representations. The existence of representations crucially depends on the analytic structure of the polynomial defining the surface as a level set in \(\mathbb {R}^{3}\).
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Open access funding provided by Linköping University. J.A would like to thank M. Aigner and A. Sykora for discussions and the Swedish Research Council for financial support.
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Arnlind, J. Low Dimensional Matrix Representations for Noncommutative Surfaces of Arbitrary Genus. Math Phys Anal Geom 23, 12 (2020). https://doi.org/10.1007/s11040-020-9333-5
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DOI: https://doi.org/10.1007/s11040-020-9333-5