VECTOR INVARIANT IDEALS OF ABELIAN GROUP ALGEBRAS UNDER THE ACTION OF THE SYMPLECTIC GROUPS
2013 ◽
Vol 12
(08)
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pp. 1350046
Keyword(s):
Let F be a finite field and let Sp 2ν(F) be the symplectic group over F. If Sp 2ν(F) acts on the F-vector space F2ν, then it can induce an action on the vector space F2ν ⊕ F2ν, defined by (x, y)A = (xA, yA), ∀ x, y ∈ F2ν, A ∈ Sp 2ν(F). If K is a field with char K ≠ char F, then Sp 2ν(F) also acts on the group algebra K[F2ν ⊕ F2ν]. In this paper, we determine the structures of Sp 2ν(F)-stable ideals of the group algebra K[F2ν ⊕ F2ν] by augmentation ideals, and describe the relations between the invariant ideals of K[F2ν] and the vector invariant ideals of K[F2ν ⊕ F2ν].
1982 ◽
Vol 33
(3)
◽
pp. 331-344
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Keyword(s):
1982 ◽
Vol 33
(3)
◽
pp. 345-350
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Keyword(s):
2002 ◽
Vol 73
(1)
◽
pp. 85-96
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2016 ◽
Vol 15
(08)
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pp. 1650150
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Keyword(s):
2008 ◽
Vol 07
(03)
◽
pp. 337-346
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Keyword(s):
1972 ◽
Vol 18
(2)
◽
pp. 149-158
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Keyword(s):
2009 ◽
Vol 87
(3)
◽
pp. 325-328
Keyword(s):
2019 ◽
Vol 18
(09)
◽
pp. 1950163
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