Algebraic Inverses on Lie Algebra Comultiplications
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In this note, we investigate algebraic loop structures and inverses of elements of a set of all homomorphisms of Lie algebras with a binary operation derived from a Lie algebra comultiplication. As a symmetry phenomenon, we show that if l ( 1 ) c and r ( 1 ) c are the left and right inverses of the identity 1 : L → L on a free graded Lie algebra L , respectively, based on the Lie algebra comultiplication ψ c : L → L ⊔ L , then we have l ( 1 ) = l ( 1 ) c and r ( 1 ) = r ( 1 ) c , where c : L → L ⊔ L is a commutator.
2011 ◽
Vol 10
(04)
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pp. 597-604
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2019 ◽
Vol 21
(07)
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pp. 1850050
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2006 ◽
Vol 05
(05)
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pp. 571-627
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2017 ◽
Vol 60
(3)
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pp. 470-477
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2020 ◽
Vol 30
(05)
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pp. 1081-1096
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1999 ◽
Vol 51
(3)
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pp. 658-672
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1999 ◽
Vol 67
(2)
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pp. 157-184
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