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Cluster Structure on Generalized Weyl Algebras

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Abstract

We introduce a class of non-commutative algebras that carry non-commutative cluster structure which are generated by identical copies of generalized Weyl algebras. Equivalent conditions for the finiteness of the set of the cluster variables of these cluster structures are provided. Mutations along with some combinatorial data, called cluster strands, arising from the cluster structure are used to construct representations of generalized Weyl algebras.

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Authors and Affiliations

  1. University of Wisconsin-Marathon, Wausau, WI, USA

    Ibrahim Saleh

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  1. Ibrahim Saleh
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Correspondence to Ibrahim Saleh.

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Presented by Paul Smith.

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Saleh, I. Cluster Structure on Generalized Weyl Algebras. Algebr Represent Theor 19, 1017–1041 (2016). https://doi.org/10.1007/s10468-016-9609-4

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  • DOI: https://doi.org/10.1007/s10468-016-9609-4

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