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1 April 2013 Abelianizations of derivation Lie algebras of the free associative algebra and the free Lie algebra
Shigeyuki Morita, Takuya Sakasai, Masaaki Suzuki
Duke Math. J. 162(5): 965-1002 (1 April 2013). DOI: 10.1215/00127094-2140560

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 theorem of Harer concerning the top rational cohomology group of the mapping class group with respect to its virtual cohomological dimension.

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Shigeyuki Morita. Takuya Sakasai. Masaaki Suzuki. "Abelianizations of derivation Lie algebras of the free associative algebra and the free Lie algebra." Duke Math. J. 162 (5) 965 - 1002, 1 April 2013. https://doi.org/10.1215/00127094-2140560

Information

Published: 1 April 2013
First available in Project Euclid: 29 March 2013

zbMATH: 1308.17021
MathSciNet: MR3047471
Digital Object Identifier: 10.1215/00127094-2140560

Subjects:
Primary: 17B56, 32G15, 55R40
Secondary: 17B65, 20J06

Rights: Copyright © 2013 Duke University Press

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Vol.162 • No. 5 • 1 April 2013
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