Author:
FISH CHRISTOPHER D.,JORDAN DAVID A.
Abstract
AbstractWe determine sufficient criteria for the prime spectrum of an ambiskew polynomial algebra R over an algebraically closed field 𝕂 to be akin to those of two of the principal examples of such an algebra, namely the universal enveloping algebra U(sl2) (in characteristic 0) and its quantization Uq(sl2) (when q is not a root of unity). More precisely, we determine sufficient criteria for the prime spectrum of R to consist of 0, the ideals (z − λ)R for some central element z of R and all λ ∈ 𝕂, and, for some positive integer d and each positive integer m, d height two prime ideals P for which R/P has Goldie rank m.
Publisher
Cambridge University Press (CUP)
Reference16 articles.
1. Connected quantized Weyl algebras and quantum cluster algebras;Fish;J. Pure Appl. Algebra,2017
2. Filter dimension of algebras and modules, a simplicity criterion of generalized weyl algebras
3. Crossed Products and Multiplicative Analogues of Weyl Algebras
4. A class of algebras similar to the enveloping algebra of sl(2, ℂ);Smith;Trans. Amer. Math. Soc.,1990