Normal Quadratics in Ore Extensions, Quantum Planes, and Quantized Weyl Algebras
环与代数
2011-08-18 v2 量子代数
摘要
Let R be a Noetherian domain and let ({\sigma}, {\delta}) be a quasi-derivation of R such that {\sigma} is an automorphism. There is an induced quasi-derivation on the classical quotient ring Q of R. Suppose F = t^2 - v is normal in the Ore extension R[t; {\sigma}, {\delta}] where v {\epsilon} R. We show F is prime in R[t; {\sigma}, {\delta}] if and only if F is irreducible in Q[t; {\sigma}, {\delta}] if and only if there does not exist w {\epsilon} Q such that v = {\sigma} (w)w - {\delta} (w). We apply this result to classify prime quadratic forms in quantum planes and quantized Weyl algebras.
引用
@article{arxiv.math/0508513,
title = {Normal Quadratics in Ore Extensions, Quantum Planes, and Quantized Weyl Algebras},
author = {Candis Holtz and Kenneth Price},
journal= {arXiv preprint arXiv:math/0508513},
year = {2011}
}