On Nichols (braided) Lie algebras
Keyword(s):
We prove (i) Nichols algebra 𝔅(V) of vector space V is finite dimensional if and only if Nichols braided Lie algebra 𝔏(V) is finite dimensional; (ii) if the rank of connected V is 2 and 𝔅(V) is an arithmetic root system, then 𝔅(V) = F ⊕ 𝔏(V); and (iii) if Δ(𝔅(V)) is an arithmetic root system and there does not exist any m-infinity element with puu ≠ 1 for any u ∈ D(V), then dim (𝔅(V)) = ∞ if and only if there exists V′, which is twisting equivalent to V, such that dim (𝔏-(V′)) = ∞. Furthermore, we give an estimation of dimensions of Nichols Lie algebras and two examples of Lie algebras which do not have maximal solvable ideals.
2007 ◽
Vol 5
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pp. 195-200
2016 ◽
Vol 2016
(716)
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2007 ◽
Vol 17
(03)
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pp. 527-555
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2019 ◽
Vol 18
(12)
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pp. 1950233
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2019 ◽
Vol 53
(supl)
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pp. 45-86
1969 ◽
Vol 21
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pp. 1432-1454
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1973 ◽
Vol 16
(1)
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pp. 54-69
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