An unabelian version of the Voronov higher bracket construction
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Martin Bordemann
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.
First of all it is a great pleasure for me to dedicate this work to Otto Kegel's 80th birthday: he was the supervisor of my master thesis in mathematics, and by his enormous patience, generosity, encouragement and his way of combining ease and utmost precision in his teaching he helped me find my way out of theoretical physics (for which I had been even less talented) towards mathematics. I should also like to thank Yaël Frégier for stimulating discussions and his well-written habilitation thesis which inspired me a lot.
© 2015 by De Gruyter
Articles in the same Issue
- Frontmatter
- I2(u)-convergence of double sequences of order (α,β)
- Regular elements of the complete semigroups of binary relations of the class Σ6(X,8)
- On the limit properties of maximal likelihood estimators in a Hilbert space
- Shadowing and average shadowing properties for iterated function systems
- On almost increasing and quasi monotone sequences
- An unabelian version of the Voronov higher bracket construction
- Necessary and sufficient conditions for the ℍ-differentiability of quaternion functions
- k-step nilpotent Lie algebras
- An optimal control problem for a system of linear hyperbolic differential equations with constant coefficients
- On topologies in the family of sets with the Baire property
- On some inequalities for functions whose absolute values of the second derivatives are α-, m-, (α,m)-logarithmically convex
- On the cardinalities of at-sets in a real Hilbert space
- Higher-order Bernoulli and poly-Bernoulli mixed type polynomials
- On the existence of solutions for nonlocal boundary value problems
- fpn-injective and fpn-flat modules
- Algebroid functions with given Borel points
Articles in the same Issue
- Frontmatter
- I2(u)-convergence of double sequences of order (α,β)
- Regular elements of the complete semigroups of binary relations of the class Σ6(X,8)
- On the limit properties of maximal likelihood estimators in a Hilbert space
- Shadowing and average shadowing properties for iterated function systems
- On almost increasing and quasi monotone sequences
- An unabelian version of the Voronov higher bracket construction
- Necessary and sufficient conditions for the ℍ-differentiability of quaternion functions
- k-step nilpotent Lie algebras
- An optimal control problem for a system of linear hyperbolic differential equations with constant coefficients
- On topologies in the family of sets with the Baire property
- On some inequalities for functions whose absolute values of the second derivatives are α-, m-, (α,m)-logarithmically convex
- On the cardinalities of at-sets in a real Hilbert space
- Higher-order Bernoulli and poly-Bernoulli mixed type polynomials
- On the existence of solutions for nonlocal boundary value problems
- fpn-injective and fpn-flat modules
- Algebroid functions with given Borel points
