Higher Braces Via Formal (Non)Commutative Geometry

  • Martin Markl
Part of the Trends in Mathematics book series (TM)


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.


Koszul braces Börjeson braces (non)commutative geometry 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Mathematical Institute of the AcademyPrague 1Czech Republic
  2. 2.Matematicko-fyzikální fakultaUniverzita KarlovaPrague 8Czech Republic

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