SCAP-subalgebras of Lie algebras

Sara Chehrazi; Ali Reza Salemkar

Czechoslovak Mathematical Journal (2016)

  • Volume: 66, Issue: 4, page 1177-1184
  • ISSN: 0011-4642

Abstract

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A subalgebra H of a finite dimensional Lie algebra L is said to be a SCAP -subalgebra if there is a chief series 0 = L 0 ⊂ L 1 ⊂ ... ⊂ L t = L of L such that for every i = 1 , 2 , ... , t , we have H + L i = H + L i - 1 or H ∩ L i = H ∩ L i - 1 . This is analogous to the concept of SCAP -subgroup, which has been studied by a number of authors. In this article, we investigate the connection between the structure of a Lie algebra and its SCAP -subalgebras and give some sufficient conditions for a Lie algebra to be solvable or supersolvable.

How to cite

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Chehrazi, Sara, and Salemkar, Ali Reza. "SCAP-subalgebras of Lie algebras." Czechoslovak Mathematical Journal 66.4 (2016): 1177-1184. <http://eudml.org/doc/287523>.

@article{Chehrazi2016,
abstract = {A subalgebra $H$ of a finite dimensional Lie algebra $L$ is said to be a $\rm SCAP$-subalgebra if there is a chief series $0=L_0\subset L_1\subset \ldots \subset L_t=L$ of $L$ such that for every $i=1,2,\ldots ,t$, we have $H+L_i=H+L_\{i-1\}$ or $H\cap L_i=H\cap L_\{i-1\}$. This is analogous to the concept of $\rm SCAP$-subgroup, which has been studied by a number of authors. In this article, we investigate the connection between the structure of a Lie algebra and its $\rm SCAP$-subalgebras and give some sufficient conditions for a Lie algebra to be solvable or supersolvable.},
author = {Chehrazi, Sara, Salemkar, Ali Reza},
journal = {Czechoslovak Mathematical Journal},
keywords = {Lie algebra; $\rm SCAP$-subalgebra; chief series; solvable; supersolvable; Lie algebra; $\text\{SCAP\}$-subalgebra; chief series; solvable; supersolvable},
language = {eng},
number = {4},
pages = {1177-1184},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {SCAP-subalgebras of Lie algebras},
url = {http://eudml.org/doc/287523},
volume = {66},
year = {2016},
}

TY - JOUR
AU - Chehrazi, Sara
AU - Salemkar, Ali Reza
TI - SCAP-subalgebras of Lie algebras
JO - Czechoslovak Mathematical Journal
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 66
IS - 4
SP - 1177
EP - 1184
AB - A subalgebra $H$ of a finite dimensional Lie algebra $L$ is said to be a $\rm SCAP$-subalgebra if there is a chief series $0=L_0\subset L_1\subset \ldots \subset L_t=L$ of $L$ such that for every $i=1,2,\ldots ,t$, we have $H+L_i=H+L_{i-1}$ or $H\cap L_i=H\cap L_{i-1}$. This is analogous to the concept of $\rm SCAP$-subgroup, which has been studied by a number of authors. In this article, we investigate the connection between the structure of a Lie algebra and its $\rm SCAP$-subalgebras and give some sufficient conditions for a Lie algebra to be solvable or supersolvable.
LA - eng
KW - Lie algebra; $\rm SCAP$-subalgebra; chief series; solvable; supersolvable; Lie algebra; $\text{SCAP}$-subalgebra; chief series; solvable; supersolvable
UR - http://eudml.org/doc/287523
ER -

References

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