2013
DOI: 10.1215/00127094-2140560
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Abelianizations of derivation Lie algebras of the free associative algebra and the free Lie algebra

Abstract: Abstract. We determine the abelianizations of the following three kinds of graded Lie algebras in certain stable ranges: derivations of the free associative algebra, derivations of the free Lie algebra and symplectic derivations of the free associative algebra. In each case, we consider both the whole derivation Lie algebra and its ideal consisting of derivations with positive degrees. As an application of the last case, and by making use of a theorem of Kontsevich, we obtain a new proof of the vanishing theor… Show more

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Cited by 18 publications
(18 citation statements)
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“…Proof. This proof is an adaptation of the proof in [25] to our context. Let G be a generator of C 1 H, that is, a basic hairy graph with one vertex.…”
Section: Theorem 77 For O = Assoc H 1 (H)[[1]] Is Generated By Trimentioning
confidence: 87%
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“…Proof. This proof is an adaptation of the proof in [25] to our context. Let G be a generator of C 1 H, that is, a basic hairy graph with one vertex.…”
Section: Theorem 77 For O = Assoc H 1 (H)[[1]] Is Generated By Trimentioning
confidence: 87%
“…In [25], Morita, Sakasai and Suzuki compute the abelianization of h. In this section, we point out how this follows from the computation of H 1 (H) and the injectivity of the trace map.…”
Section: The Abelianization Of Hmentioning
confidence: 99%
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“…While this holds true for k = 1 [20,43], Theorem 5.1 shows that it is wrong for k = 2. Morita, Sakasai and Suzuki [44] pointed out that Conjecture 5.2 is implied by a more general conjecture made by Kontsevich around 25 years ago [37].…”
mentioning
confidence: 99%