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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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