Extensions and automorphisms of Lie algebras
2016 ◽
Vol 16
(09)
◽
pp. 1750162
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Keyword(s):
Let [Formula: see text] be a short exact sequence of Lie algebras over a field [Formula: see text], where [Formula: see text] is abelian. We show that the obstruction for a pair of automorphisms in [Formula: see text] to be induced by an automorphism in [Formula: see text] lies in the Lie algebra cohomology [Formula: see text]. As a consequence, we obtain a four term exact sequence relating automorphisms, derivations and cohomology of Lie algebras. We also obtain a more explicit necessary and sufficient condition for a pair of automorphisms in [Formula: see text] to be induced by an automorphism in [Formula: see text], where [Formula: see text] is a free nilpotent Lie algebra of rank [Formula: see text] and step [Formula: see text].
2012 ◽
Vol 11
(01)
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pp. 1250011
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2019 ◽
Vol 12
(02)
◽
pp. 1950028
1967 ◽
Vol 19
◽
pp. 1250-1258
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2018 ◽
Vol 28
(01)
◽
pp. 115-131
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2011 ◽
Vol 08
(05)
◽
pp. 929-935
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