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论文类型：期刊论文

发表时间：2016-12-01

发表刊物：CZECHOSLOVAK MATHEMATICAL JOURNAL

收录刊物：SCIE、Scopus

卷号：66

期号：4

页面范围：1059-1078

ISSN号：0011-4642

关键字：vector invariant ideal; group algebra; unitary group; orthogonal group

摘要：Let F be a finite field of characteristic p and K a field which contains a primitive pth root of unity and char K not equal p. Suppose that a classical group G acts on the F-vector space V. Then it can induce the actions on the vector space V V and on the group algebra K[V V], respectively. In this paper we determine the structure of G-invariant ideals of the group algebra K[V V], and establish the relationship between the invariant ideals of K[V] and the vector invariant ideals of K[V V], if G is a unitary group or orthogonal group. Combining the results obtained by Nan and Zeng (2013), we solve the problem of vector invariant ideals for all classical groups over finite fields.