Discriminants of Taft Algebra Smash Products and Applications
Discriminants of Taft Algebra Smash Products and Applications
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DOI：
10.1007/s10468-018-9798-0
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发表时间：
2017-07
影响因子：
0.6
通讯作者：
Jason Gaddis;R. Won;Daniel Yee
中科院分区：
文献类型：
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作者：
Jason Gaddis;R. Won;Daniel Yee
给出了Taft代数Smash积的中心为不动环的一般判据。并将其应用于非对易判别式的研究。我们的方法依赖于Nguyen，Trampel和Yakimov的Poisson方法，但也利用了Poisson Ore推广。具体地说，我们充分确定了Taft代数在量子平面和量子Weyl代数上的内在忠实作用。我们计算了相应的Smash积的判别式，并将其应用于计算Azumaya轨迹和限制自同构群。
A general criterion is given for when the center of a Taft algebra smash product is the fixed ring. This is applied to the study of the noncommutative discriminant. Our method relies on the Poisson methods of Nguyen, Trampel, and Yakimov, but also makes use of Poisson Ore extensions. Specifically, we fully determine the inner faithful actions of Taft algebras on quantum planes and quantum Weyl algebras. We compute the discriminant of the corresponding smash product and apply it to compute the Azumaya locus and restricted automorphism group.