| Title:
|
Homomorphisms from the unitary group to the general linear group over complex number field and applications (English) |
| Author:
|
Cao, Chong-Guang |
| Author:
|
Zhang, Xian |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
38 |
| Issue:
|
3 |
| Year:
|
2002 |
| Pages:
|
209-217 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $M_n$ be the multiplicative semigroup of all $n\times n$ complex matrices, and let $U_n$ and $GL_n$ be the $n$–degree unitary group and general linear group over complex number field, respectively. We characterize group homomorphisms from $U_n$ to $GL_m$ when $n>m\ge 1$ or $n=m\ge 3$, and thereby determine multiplicative homomorphisms from $U_n$ to $M_m$ when $n>m\ge 1$ or $n=m\ge 3$. This generalize Hochwald’s result in [Lin. Alg. Appl. 212/213:339-351(1994)]: if $f:U_n\rightarrow M_n$ is a spectrum–preserving multiplicative homomorphism, then there exists a matrix $R$ in $GL_n$ such that $ f(A)={R}AR$ for any $A\in U_n$. (English) |
| Keyword:
|
homomorphism |
| Keyword:
|
unitary group |
| Keyword:
|
general linear group |
| MSC:
|
15A30 |
| MSC:
|
20E36 |
| MSC:
|
20G20 |
| idZBL:
|
Zbl 1068.20048 |
| idMR:
|
MR1921592 |
| . |
| Date available:
|
2008-06-06T22:30:29Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107834 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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