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Homotopy Batalin-Vilkovisky Algebras

Author
Galvez, M.; Tonks, A.; Vallette, B.
Type of activity
Journal article
Journal
Journal of noncommutative geometry
Date of publication
2012
Volume
6
Number
3
First page
539
Last page
602
DOI
https://doi.org/10.4171/JNCG/99 Open in new window
Repository
http://hdl.handle.net/2117/16804 Open in new window
URL
http://www.ems-ph.org/journals/show_pdf.php?issn=1661-6952&vol=6&iss=3&rank=4 Open in new window
Abstract
This paper provides an explicit cofibrant resolution of the operad encoding Batalin-Vilkovisky algebras. Thus it defines the notion of homotopy Batalin-Vilkovisky algebras with the required homotopy properties. To define this resolution, we extend the theory of Koszul duality to operads and properads that are defined by quadratic and linear relations. The operad encoding Batalin-Vilkovisky algebras is shown to be Koszul in this sense. This allows us to prove a Poincaré-Birkhoff-Witt Theorem for...
Citation
Galvez, M.; Tonks, A.; Vallette, B. Homotopy Batalin-Vilkovisky Algebras. "Journal of noncommutative geometry", 2012, vol. 6, núm. 3, p. 539-602.
Keywords
Batalin-Vilkovisky algebra, Gerstenhaber algebra, Koszul duality theory, Maurer-Cartan equation, homotopy algebras, operad framed little disc, topological conformal field theory, vertex algebras
Group of research
GEOMVAP - Geometry of Manifolds and Applications

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