双斜多项式环上的Hopf–Galois结构

IF 0.7 2区数学 Q2 MATHEMATICS Journal of Noncommutative Geometry Pub Date : 2019-10-31 DOI:10.4171/jncg/441

J. Bichon, Agust'in Garc'ia Iglesias

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引用次数: 1

摘要

给出了将代数R上的Hopf-Galois代数结构扩展到基于R的广义双基环上的充分必要条件，使扩展的附加变量在适当意义上是斜基元的。在合适的Hopf代数H(R)的基础上，证明了所关联的Hopf代数又是一个广义的双置环。研究了几个例子，包括Uq(sl2)上的Hopf-Galois对象。

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Hopf–Galois structures on ambiskew polynomial rings

We provide necessary and sufficient conditions to extend the Hopf-Galois algebra structure on an algebra R to a generalized ambiskew ring based on R, in a way such that the added variables for the extension are skew-primitive in an appropriate sense. We show that the associated Hopf algebra is again a a generalized ambiskew ring, based on a suitable Hopf algebra H(R). Several examples are examined, including the Hopf-Galois objects over Uq(sl2).

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来源期刊

Journal of Noncommutative Geometry 数学-数学

CiteScore

1.60

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Noncommutative Geometry covers the noncommutative world in all its aspects. It is devoted to publication of research articles which represent major advances in the area of noncommutative geometry and its applications to other fields of mathematics and theoretical physics. Topics covered include in particular: Hochschild and cyclic cohomology K-theory and index theory Measure theory and topology of noncommutative spaces, operator algebras Spectral geometry of noncommutative spaces Noncommutative algebraic geometry Hopf algebras and quantum groups Foliations, groupoids, stacks, gerbes Deformations and quantization Noncommutative spaces in number theory and arithmetic geometry Noncommutative geometry in physics: QFT, renormalization, gauge theory, string theory, gravity, mirror symmetry, solid state physics, statistical mechanics.