The groups of automorphisms of the Lie algebras of polynomial vector fields with zero or constant divergence
Bavula, V.V.
(2017)
The groups of automorphisms of the Lie algebras of polynomial vector fields with zero or constant divergence.
Communications in Algebra, 45 (3).
pp. 1114-1133.
ISSN 0092-7872
Abstract
Let Pn = K[x1, . . . , xn] be a polynomial algebra over a eld K of characteristic
zero and div0
n
(respectively, divc
n
) be the Lie algebra of derivations of Pn
with zero (respectively, constant) divergence. We prove that AutLie(div0
n
) ≃
AutK−alg(Pn) (n ≥ 2) and AutLie(divc
n
) ≃ AutK−alg(Pn). The Lie algebra divc
n
is a maximal Lie subalgebra of DerK (Pn). Minimal nite sets of generators are
found for the Lie algebras div0
n
and divc
n
.
Metadata
Authors/Creators:
Bavula, V.V.
Copyright, Publisher and Additional Information:
This is an Accepted Manuscript of an article published by Taylor & Francis in Communications in Algebra on 7 Oct 2016 available online: https://doi.org/10.1080/00927872.2016.1175596.
Keywords:
Automorphism; derivation;
group of automorphisms; Lie
algebra; locally nilpotent
derivation; the divergence;
the Lie algebras of
polynomial vector elds with
zero or constant divergence
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