交叉积群代数有限维数问题的一点注记

数学物理学报 ›› 2014, Vol. 34 ›› Issue (3): 638-642.

交叉积群代数有限维数问题的一点注记

张棉棉¹|曹海军²

1.杭州师范大学数学系杭州 310036;
2.山东交通学院理学院济南 |250357

收稿日期:2013-01-15 修回日期:2014-03-26 出版日期:2014-06-25 发布日期:2014-06-25
基金资助:
国家自然科学基金(11026207, 11226065)、浙江省自然科学基金(Y6100173, Y12A010086, LQ12A01028)和山东交通学院科研启动金资助

A Note on the Finitistic Dimension of Crossed Product Group Algebras

ZHANG Mian-Mian¹, CAO Hai-Jun²

1.The Department of Mathematics, Hangzhou Normal University, Hangzhou 310036;
2.School of Science, Shandong Jiaotong University, Jinan 250357

Received:2013-01-15 Revised:2014-03-26 Online:2014-06-25 Published:2014-06-25
Supported by:
国家自然科学基金(11026207, 11226065)、浙江省自然科学基金(Y6100173, Y12A010086, LQ12A01028)和山东交通学院科研启动金资助

摘要/Abstract

摘要：

设G是一个有限群, k是一个代数闭域且k$的特征不整除G的阶. ∧是一个扭kG -模代数, ∧*G是一个交叉积代数. 该文证明∧*G和∧具有相同的有限维数, 且同时满足有限维数猜想定理.

关键词: 交叉积群代数, 有限维数猜想

Abstract:

Let G be a finite group, k be an algebraically closed field whose characteristic does not divide the order of G, and
∧ be a twisted kG-module algebra such that ∧*G exists as a crossed product algebra. We show that the finitistic
dimensions of ∧*G and ∧ are same and ∧*G satisfies the finitistic dimension conjecture if and only if ∧ does.

Key words: Crossed product algebras, Finitistic dimension

中图分类号:

16G10

张棉棉, 曹海军. 交叉积群代数有限维数问题的一点注记[J]. 数学物理学报, 2014, 34(3): 638-642.

ZHANG Mian-Mian, CAO Hai-Jun. A Note on the Finitistic Dimension of Crossed Product Group Algebras[J]. Acta mathematica scientia,Series A, 2014, 34(3): 638-642.

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