| Title:
|
Composition-diamond lemma for modules (English) |
| Author:
|
Chen, Yuqun |
| Author:
|
Chen, Yongshan |
| Author:
|
Zhong, Chanyan |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
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60 |
| Issue:
|
1 |
| Year:
|
2010 |
| Pages:
|
59-76 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We investigate the relationship between the Gröbner-Shirshov bases in free associative algebras, free left modules and "double-free" left modules (that is, free modules over a free algebra). We first give Chibrikov's Composition-Diamond lemma for modules and then we show that Kang-Lee's Composition-Diamond lemma follows from it. We give the Gröbner-Shirshov bases for the following modules: the highest weight module over a Lie algebra $sl_2$, the Verma module over a Kac-Moody algebra, the Verma module over the Lie algebra of coefficients of a free conformal algebra, and a universal enveloping module for a Sabinin algebra. As applications, we also obtain linear bases for the above modules. (English) |
| Keyword:
|
Gröbner-Shirshov basis |
| Keyword:
|
module |
| Keyword:
|
Lie algebra |
| Keyword:
|
Kac-Moody algebra |
| Keyword:
|
conformal algebra |
| Keyword:
|
Sabinin algebra |
| MSC:
|
13P10 |
| MSC:
|
16D10 |
| MSC:
|
16S15 |
| MSC:
|
17A01 |
| MSC:
|
17B67 |
| idZBL:
|
Zbl 1224.16046 |
| idMR:
|
MR2595070 |
| . |
| Date available:
|
2010-07-20T16:14:20Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140549 |
| . |
| Reference:
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