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Journal of the London Mathematical Society 1988 s2-38(1):47-55; doi:10.1112/jlms/s2-38.1.47
© 1988 by London Mathematical Society
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© Oxford University Press

Crossed Products and Multiplicative Analogues of Weyl Algebras

J. C. McConnell and J. J. Pettit

School of Mathematics, University of Leeds Leeds LS2 9JT

We consider a class of algebras (defined via multiplicative commutators) which generalise the ‘canonical commutation relation’ xy = {lambda}yx of quantum mechanics. The corresponding algebras defined via additive commutators are closely related to the Weyl algebras. We show that these multiplicative algebras behave very differently from the Weyl algebras, and use them to give examples of hereditary Noetherian affine algebras of large Gelfand-Kirillov dimension.


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