Vector invariant ideals of abelian group algebras under the actions of the unitary groups and orthogonal groups
Czechoslovak Mathematical Journal, Tome 66 (2016) no. 4, pp. 1059-1078.
Voir la notice de l'article dans Czech Digital Mathematics Library
Let $F$ be a finite field of characteristic $p$ and $K$ a field which contains a primitive $p$th root of unity and ${\rm char} K\neq p$. Suppose that a classical group $G$ acts on the $F$-vector space $V$. Then it can induce the actions on the vector space $V\oplus V$ and on the group algebra $K[V\oplus V]$, respectively. In this paper we determine the structure of $G$-invariant ideals of the group algebra $K[V\oplus V]$, and establish the relationship between the invariant ideals of $K[V]$ and the vector invariant ideals of $K[V\oplus V]$, 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.
DOI :
10.1007/s10587-016-0310-x
Classification :
16S34, 20G40
Mots-clés : vector invariant ideal; group algebra; unitary group; orthogonal group
Mots-clés : vector invariant ideal; group algebra; unitary group; orthogonal group
@article{10_1007_s10587_016_0310_x, author = {Zeng, Lingli and Nan, Jizhu}, title = {Vector invariant ideals of abelian group algebras under the actions of the unitary groups and orthogonal groups}, journal = {Czechoslovak Mathematical Journal}, pages = {1059--1078}, publisher = {mathdoc}, volume = {66}, number = {4}, year = {2016}, doi = {10.1007/s10587-016-0310-x}, mrnumber = {3572923}, zbl = {06674862}, language = {en}, url = {https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-016-0310-x/} }
TY - JOUR AU - Zeng, Lingli AU - Nan, Jizhu TI - Vector invariant ideals of abelian group algebras under the actions of the unitary groups and orthogonal groups JO - Czechoslovak Mathematical Journal PY - 2016 SP - 1059 EP - 1078 VL - 66 IS - 4 PB - mathdoc UR - https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-016-0310-x/ DO - 10.1007/s10587-016-0310-x LA - en ID - 10_1007_s10587_016_0310_x ER -
%0 Journal Article %A Zeng, Lingli %A Nan, Jizhu %T Vector invariant ideals of abelian group algebras under the actions of the unitary groups and orthogonal groups %J Czechoslovak Mathematical Journal %D 2016 %P 1059-1078 %V 66 %N 4 %I mathdoc %U https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-016-0310-x/ %R 10.1007/s10587-016-0310-x %G en %F 10_1007_s10587_016_0310_x
Zeng, Lingli; Nan, Jizhu. Vector invariant ideals of abelian group algebras under the actions of the unitary groups and orthogonal groups. Czechoslovak Mathematical Journal, Tome 66 (2016) no. 4, pp. 1059-1078. doi : 10.1007/s10587-016-0310-x. https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-016-0310-x/
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