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个人信息Personal Information
教授
博士生导师
硕士生导师
性别：男
毕业院校：哈尔滨工业大学
学位：博士
所在单位：数学科学学院
电子邮箱：jznan@dlut.edu.cn
VECTOR INVARIANT IDEALS OF ABELIAN GROUP ALGEBRAS UNDER THE ACTION OF THE SYMPLECTIC GROUPS
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论文类型：期刊论文
发表时间：2013-12-01
发表刊物：JOURNAL OF ALGEBRA AND ITS APPLICATIONS
收录刊物：SCIE、Scopus
卷号：12
期号：8
ISSN号：0219-4988
关键字：Vector invariant ideal; group algebra; symplectic group; group action
摘要：Let F be a finite field and let Sp(2v) (F) be the symplectic group over F. If Sp(2v) (F) acts on the F-vector space F-2v, then it can induce an action on the vector space F-2v circle plus F-2v, defined by (x, y)(A) = (xA, yA), for all x, y is an element of F-2v, A is an element of Sp(2v) (F). If K is a field with char K not equal char F, then Sp(2v) (F) also acts on the group algebra K[F-2v circle plus F-2v]. In this paper, we determine the structures of Sp(2v) (F)-stable ideals of the group algebra K[F-2v circle plus F-2v] by augmentation ideals, and describe the relations between the invariant ideals of K[F-2v] and the vector invariant ideals of K[F-2v circle plus F-2v].