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q-analogs of harmonic oscillators and related rings

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Abstract

A ringH q which is aq-analog of the universal enveloping algebra of the Heisenberg Lie algebraU(h) is constructed, and its ring theoretic properties are studied. It is shown thatH q has a factor ringA q which is a simple domain with properties that are compared to the Weyl algebra. A secondq-analogH q ofU(h) is constructed, andH q is shown to be a primitive ring.

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Authors and Affiliations

  1. Department of Mathematics, Wake Forest University, Box 7311, 27109, Winston-Salem, NC

    Ellen E. Kirkman

  2. Department of Mathematics 0112, University of California, San Diego, 92093-0112, La Jolla, CA

    Lance W. Small

Authors
  1. Ellen E. Kirkman
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  2. Lance W. Small
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Correspondence to Ellen E. Kirkman.

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Kirkman, E.E., Small, L.W. q-analogs of harmonic oscillators and related rings. Israel J. Math. 81, 111–127 (1993). https://doi.org/10.1007/BF02761300

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