教育与研究

Hopf-Galois 扩张下的 Ding 投射维数的研究

杨 淑静

重庆师范大学 数学科学学院

DOI: https://doi.org/10.59429/jyyj.v6i10.7804

Keywords: Hopf-Galois 扩张；Ding 投射模；Ding 投射维数；整体 Ding 投射维数；有限 Ding 投射维数

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Abstract

设 H 为半单 Hopf 代数，A 为给定域 k 上的代数，B 为 A 的子代数且 A/B 为 Hopf 代数 H 上的 Hopf-Galois 扩张。论文主要考虑 Hopf-Galois 扩张下的 Ding 投射模及其维数，并将其应用到 Crossed product A#σ H 与 Twisted smash product A∗ H 中，可得它们的整体 Ding 投射维数和有限 Ding 投射维数不超过 A 的整体 Ding 投射维数和有限 Ding 投射维数。

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