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An unabelian version of the Voronov higher bracket construction

An unabelian version of the Voronov higher bracket construction Abstract In this paper, we show how to extend Voronov's construction of L ∞ -structures by using the splitting of a graded Lie algebra into the direct vector space sum of two subalgebras, of which one is abelian, to just a graded Lie algebra inclusion without an algebraic complement. The construction uses certain Verma modules of the universal enveloping algebra of the graded Lie algebra, and it is fairly explicit in terms of convolution formulas. Voronov's result (J. Pure Appl. Algebra 202 (2005), 133–153) and Bandiera's result on nonabelian complements ( http://arxiv.org/abs/1304.4097 ) occur as particular cases. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Georgian Mathematical Journal de Gruyter

An unabelian version of the Voronov higher bracket construction

Georgian Mathematical Journal , Volume 22 (2) – Jun 1, 2015

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Publisher
de Gruyter
Copyright
Copyright © 2015 by the
ISSN
1072-947X
eISSN
1572-9176
DOI
10.1515/gmj-2015-0021
Publisher site
See Article on Publisher Site

Abstract

Abstract In this paper, we show how to extend Voronov's construction of L ∞ -structures by using the splitting of a graded Lie algebra into the direct vector space sum of two subalgebras, of which one is abelian, to just a graded Lie algebra inclusion without an algebraic complement. The construction uses certain Verma modules of the universal enveloping algebra of the graded Lie algebra, and it is fairly explicit in terms of convolution formulas. Voronov's result (J. Pure Appl. Algebra 202 (2005), 133–153) and Bandiera's result on nonabelian complements ( http://arxiv.org/abs/1304.4097 ) occur as particular cases.

Journal

Georgian Mathematical Journalde Gruyter

Published: Jun 1, 2015

There are no references for this article.