On matrix Lie rings over a commutative ring that contain the special linear Lie ring

Evgenii L. Bashkirov; Esra Pekönür

Commentationes Mathematicae Universitatis Carolinae (2016)

  • Volume: 57, Issue: 1, page 1-6
  • ISSN: 0010-2628

Abstract

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Let K be an associative and commutative ring with 1 , k a subring of K such that 1 ∈ k , n ≥ 2 an integer. The paper describes subrings of the general linear Lie ring g l n ( K ) that contain the Lie ring of all traceless matrices over k .

How to cite

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Bashkirov, Evgenii L., and Pekönür, Esra. "On matrix Lie rings over a commutative ring that contain the special linear Lie ring." Commentationes Mathematicae Universitatis Carolinae 57.1 (2016): 1-6. <http://eudml.org/doc/276802>.

@article{Bashkirov2016,
abstract = {Let $K$ be an associative and commutative ring with $1$, $k$ a subring of $K$ such that $1\in k$, $n\ge 2$ 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 $k$.},
author = {Bashkirov, Evgenii L., Pekönür, Esra},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Lie rings; commutative associative rings},
language = {eng},
number = {1},
pages = {1-6},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On matrix Lie rings over a commutative ring that contain the special linear Lie ring},
url = {http://eudml.org/doc/276802},
volume = {57},
year = {2016},
}

TY - JOUR
AU - Bashkirov, Evgenii L.
AU - Pekönür, Esra
TI - On matrix Lie rings over a commutative ring that contain the special linear Lie ring
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2016
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 57
IS - 1
SP - 1
EP - 6
AB - Let $K$ be an associative and commutative ring with $1$, $k$ a subring of $K$ such that $1\in k$, $n\ge 2$ 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 $k$.
LA - eng
KW - Lie rings; commutative associative rings
UR - http://eudml.org/doc/276802
ER -

References

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  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. MR2397770
  2. Bashkirov E.L., Matrix Lie rings that contain an abelian subring, J. Prime Res. Math. 4 (2008), 113–117. MR2490007
  3. Wang D.Y., Extensions of Lie algebras according to the extension of fields, J. Math. Res. Exposition 25 (2005), no. 3, 543–547. MR2163737
  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. MR2541763
  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. MR1320525

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