The Prime and Primitive Spectra of Multiparameter Quantum Symplectic and Euclidean Spaces

Abstract

We investigate a class of algebras that provides multiparameter versions of both quantum symplectic space and quantum Euclidean 2n-space. These algebras encompass the graded quantized Weyl algebras, the quantized Heisenberg space, and a class of algebras introduced by Oh. We describe the structure of the prime and primitive ideals of these algebras. Other structural results include normal separation and catenarity.

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Acknowledgments

This work forms a portion of the author's PhD thesis at the University of California, Santa Barbara. She would like to thank her advisor, K. R. Goodearl, for his invaluable guidance and direction. The author would also like to express her gratitude to the referee for several helpful suggestions and comments, which have greatly improved this paper.