Non-Commutative Batalin-Vilkovisky Algebras, Homotopy Lie Algebras and the Courant Bracket

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dc.creatorBering, K.
dc.date2006-03-15
dc.date2007-01-30
dc.date.accessioned2026-07-07T10:46:13Z
dc.date.available2026-07-07T10:46:13Z
dc.descriptionWe consider two different constructions of higher brackets. First, based on a Grassmann-odd, nilpotent Δoperator, we define a non-commutative generalization of the higher Koszul brackets, which are used in a generalized Batalin-Vilkovisky algebra, and we show that they form a homotopy Lie algebra. Secondly, we investigate higher, so-called derived brackets built from symmetrized, nested Lie brackets with a fixed nilpotent Lie algebra element Q. We find the most general Jacobi-like identity that such a hierarchy satisfies. The numerical coefficients in front of each term in these generalized Jacobi identities are related to the Bernoulli numbers. We suggest that the definition of a homotopy Lie algebra should be enlarged to accommodate this important case. Finally, we consider the Courant bracket as an example of a derived bracket. We extend it to the "big bracket" of exterior forms and multi-vectors, and give closed formulas for the higher Courant brackets.
dc.description42 pages, LaTeX. v2: Added remarks in Section 5. v3: Added further explanation. v4: Minor adjustments. v5: Section 5 completely rewritten to include covariant construction. v6: Minor adjustments. v7: Added references and explanation to Section 5
dc.identifierhttps://arxiv.org/abs/hep-th/0603116
dc.identifierhttp://arxiv.org/abs/hep-th/0603116
dc.identifierCommun.Math.Phys.274:297-341,2007
dc.identifierdoi:10.1007/s00220-007-0278-3
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/183157
dc.subjectHigh Energy Physics - Theory
dc.subjectQuantum Algebra
dc.titleNon-Commutative Batalin-Vilkovisky Algebras, Homotopy Lie Algebras and the Courant Bracket
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