New York Journal of Mathematics
Volume 19 (2013) 39-50


Benton L. Duncan

Operator algebras associated to integral domains

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Published: February 12, 2013
Keywords: Integral domains, semicrossed products
Subject: 47L74, 47L40

We study operator algebras associated to integral domains. In particular, with respect to a set of natural identities we look at the possible nonselfadjoint operator algebras which encode the ring structure of an integral domain. We show that these algebras give a new class of examples of semicrossed products by discrete semigroups. We investigate the structure of these algebras together with a particular class of representations.

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Department of Mathematics, North Dakota State University, Fargo, North Dakota, USA