| Title:
|
Vector invariant ideals of abelian group algebras under the actions of the unitary groups and orthogonal groups (English) |
| Author:
|
Zeng, Lingli |
| Author:
|
Nan, Jizhu |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
66 |
| Issue:
|
4 |
| Year:
|
2016 |
| Pages:
|
1059-1078 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
vector invariant ideal |
| Keyword:
|
group algebra |
| Keyword:
|
unitary group |
| Keyword:
|
orthogonal group |
| MSC:
|
16S34 |
| MSC:
|
20G40 |
| idZBL:
|
Zbl 06674862 |
| idMR:
|
MR3572923 |
| DOI:
|
10.1007/s10587-016-0310-x |
| . |
| Date available:
|
2016-11-26T20:50:03Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145919 |
| . |
| Reference:
|
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| Reference:
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