Leibniz A -algebras

David A. Towers

Communications in Mathematics (2020)

  • Volume: 28, Issue: 2, page 103-121
  • ISSN: 1804-1388

Abstract

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A finite-dimensional Lie algebra is called an A -algebra if all of its nilpotent subalgebras are abelian. These arise in the study of constant Yang-Mills potentials and have also been particularly important in relation to the problem of describing residually finite varieties. They have been studied by several authors, including Bakhturin, Dallmer, Drensky, Sheina, Premet, Semenov, Towers and Varea. In this paper we establish generalisations of many of these results to Leibniz algebras.

How to cite

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Towers, David A.. "Leibniz $A$-algebras." Communications in Mathematics 28.2 (2020): 103-121. <http://eudml.org/doc/296990>.

@article{Towers2020,
abstract = {A finite-dimensional Lie algebra is called an $A$-algebra if all of its nilpotent subalgebras are abelian. These arise in the study of constant Yang-Mills potentials and have also been particularly important in relation to the problem of describing residually finite varieties. They have been studied by several authors, including Bakhturin, Dallmer, Drensky, Sheina, Premet, Semenov, Towers and Varea. In this paper we establish generalisations of many of these results to Leibniz algebras.},
author = {Towers, David A.},
journal = {Communications in Mathematics},
keywords = {Lie algebras; Leibniz algebras; $A$-algebras; Frattini ideal; solvable; nilpotent; completely solvable; metabelian; monolithic; cyclic Leibniz algebras},
language = {eng},
number = {2},
pages = {103-121},
publisher = {University of Ostrava},
title = {Leibniz $A$-algebras},
url = {http://eudml.org/doc/296990},
volume = {28},
year = {2020},
}

TY - JOUR
AU - Towers, David A.
TI - Leibniz $A$-algebras
JO - Communications in Mathematics
PY - 2020
PB - University of Ostrava
VL - 28
IS - 2
SP - 103
EP - 121
AB - A finite-dimensional Lie algebra is called an $A$-algebra if all of its nilpotent subalgebras are abelian. These arise in the study of constant Yang-Mills potentials and have also been particularly important in relation to the problem of describing residually finite varieties. They have been studied by several authors, including Bakhturin, Dallmer, Drensky, Sheina, Premet, Semenov, Towers and Varea. In this paper we establish generalisations of many of these results to Leibniz algebras.
LA - eng
KW - Lie algebras; Leibniz algebras; $A$-algebras; Frattini ideal; solvable; nilpotent; completely solvable; metabelian; monolithic; cyclic Leibniz algebras
UR - http://eudml.org/doc/296990
ER -

References

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