Abstract
We translate the main result of [11] to the language of formal geometry. In this new setting we prove directly that the Koszul resp. Börjeson braces are pullbacks of linear vector fields over the formal automorphism \(\varphi(a)=\mathrm{exp}(a)-1\) in the Koszul, resp. \(\varphi(a)=a(1-a)^{-1}\) in the Börjeson case. We then argue that both braces are versions of the same object, once materialized in the world of formal commutative geometry, once in the noncommutative one.
Mathematics Subject Classification (2010). 13D99, 14A22, 55S20
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© 2015 Springer International Publishing Switzerland
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Markl, M. (2015). Higher Braces Via Formal (Non)Commutative Geometry. In: Kielanowski, P., Bieliavsky, P., Odzijewicz, A., Schlichenmaier, M., Voronov, T. (eds) Geometric Methods in Physics. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-18212-4_4
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DOI: https://doi.org/10.1007/978-3-319-18212-4_4
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-18211-7
Online ISBN: 978-3-319-18212-4
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