Vector invariant ideals of abelian group algebras under the actions of the unitary groups and orthogonal groups
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Let F be a finite field of characteristic p and K a field which contains a primitive pth root of unity and char K ≠ 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.
Keywordsvector invariant ideal group algebra unitary group orthogonal group
MSC 201016S34 20G40
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- J. Nan, L. Zeng: Vector invariant ideals of abelian group algebras under the action of the symplectic groups. J. Algebra Appl. 12 (2013), Article ID 1350046, 12 pages.Google Scholar
© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2016