A Remark on Ado's Theorem for Principal Ideal Domains
Journal of Lie Theory, Tome 34 (2024) no. 3, pp. 531-540
Voir la notice de l'article provenant de la source Heldermann Verlag
Ado's Theorem had been extended to principal ideal domains independently by Churkin and Weigel. They proved that if R is a principal ideal domain of characteristic zero and L is a Lie algebra over R which is also a free R-module of finite rank, then L admits a finite faithful Lie algebra representation over R. We present a quantitative proof of this result, providing explicit bounds on the degree of the Lie algebra representations in terms of the rank as a free module. To achieve it, we generalise an established embedding theorem for complex Lie algebras: any Lie algebra as above embeds in a larger Lie algebra that decomposes as the direct sum of its nilpotent radical and another subalgebra.
Classification :
17B10, 17B30, 17B35
Mots-clés : Ado's Theorem, Lie algebras, degree of representations
Mots-clés : Ado's Theorem, Lie algebras, degree of representations
Affiliations des auteurs :
Andoni Zozaya 1
Andoni Zozaya. A Remark on Ado's Theorem for Principal Ideal Domains. Journal of Lie Theory, Tome 34 (2024) no. 3, pp. 531-540. http://geodesic.mathdoc.fr/item/JOLT_2024_34_3_a2/
@article{JOLT_2024_34_3_a2,
author = {Andoni Zozaya},
title = {A {Remark} on {Ado's} {Theorem} for {Principal} {Ideal} {Domains}},
journal = {Journal of Lie Theory},
pages = {531--540},
year = {2024},
volume = {34},
number = {3},
url = {http://geodesic.mathdoc.fr/item/JOLT_2024_34_3_a2/}
}