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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.
Georgian Mathematical Journal – de Gruyter
Published: Jun 1, 2015
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