| Title:
|
On matrix Lie rings over a commutative ring that contain the special linear Lie ring (English) |
| Author:
|
Bashkirov, Evgenii L. |
| Author:
|
Pekönür, Esra |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
57 |
| Issue:
|
1 |
| Year:
|
2016 |
| Pages:
|
1-6 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $K$ be an associative and commutative ring with $1$, $k$ a subring of $K$ such that $1\in k$, $n\geq 2$ an integer. The paper describes subrings of the general linear Lie ring $gl_{n} ( K )$ that contain the Lie ring of all traceless matrices over $k$. (English) |
| Keyword:
|
Lie rings |
| Keyword:
|
commutative associative rings |
| MSC:
|
17B05 |
| MSC:
|
17B99 |
| idZBL:
|
Zbl 06562191 |
| idMR:
|
MR3478334 |
| DOI:
|
10.14712/1213-7243.2015.144 |
| . |
| Date available:
|
2016-04-12T04:59:31Z |
| Last updated:
|
2020-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144908 |
| . |
| Reference:
|
[1] Bashkirov E.L.: Matrix Lie rings that contain a one-dimensional Lie algebra of semi-simple matrices.J. Prime Res. Math. 3 (2007), 111–119. MR 2397770 |
| Reference:
|
[2] Bashkirov E.L.: Matrix Lie rings that contain an abelian subring.J. Prime Res. Math. 4 (2008), 113–117. MR 2490007 |
| Reference:
|
[3] Wang D.Y.: Extensions of Lie algebras according to the extension of fields.J. Math. Res. Exposition 25 (2005), no. 3, 543–547. MR 2163737 |
| Reference:
|
[4] Zhao Y.X., Wang D.Y., Wang Ch.H.: Intermediate Lie algebras between the symplectic algebras and the general linear Lie algebras over commutative rings.J. Math. (Wuhan) 29 (2009), no. 3, 247-252. MR 2541763 |
| Reference:
|
[5] Vavilov N.A.: Intermediate subgroups in Chevalley groups.Groups of Lie Type and Their Geometries (Como 1993), London Math. Soc. Lecture Note Ser., 207, Cambridge Univ. Press, Cambridge, 1995, pp. 233–280. MR 1320525 |
| . |
