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RESEARCH PRODUCT

Some criteria for detecting capable Lie algebras

Francesco G. RussoPeyman NiroomandMohsen Parvizi

subject

Discrete mathematicsPure mathematicsAlgebra and Number TheoryHeisenberg algebraNon-associative algebranilpotent Lie algebrasKilling formAffine Lie algebraGraded Lie algebraLie conformal algebraNilpotent Lie algebraSettore MAT/02 - AlgebraAdjoint representation of a Lie algebraRepresentation of a Lie groupcorankHomology of Lie algebraMathematics

description

Abstract In virtue of a recent bound obtained in [P. Niroomand, F.G. Russo, A note on the Schur multiplier of a nilpotent Lie algebra, Comm. Algebra 39 (2011) 1293–1297], we classify all capable nilpotent Lie algebras of finite dimension possessing a derived subalgebra of dimension one. Indirectly, we find also a criterion for detecting noncapable Lie algebras. The final part contains a construction, which shows that there exist capable Lie algebras of arbitrary big corank (in the sense of Berkovich–Zhou).

yearjournalcountryeditionlanguage
2013-06-01Journal of Algebra
https://doi.org/10.1016/j.jalgebra.2013.02.033