2013/09/30 by Markl, Martin · 1 citation
#13D99 #55S20 #Algebraic Topology (math.AT) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #K-Theory and Homology (math.KT) #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.1309.7744
In Part I we show that the classical Koszul braces, as well as their non-commutative counterparts constructed recently by Borjeson, are the twistings of the trivial L-infinity- (resp. A-infinity-) algebra by a specific automorphism. This gives an astonishingly simple proof of their properties. Using the twisting, we construct other surprising examples of braces. We finish Part 1 by discussing C-infinity-braces related to Lie algebras. In Part 2 we prove that in fact all natural braces are the twistings by unique automorphisms. We also show that there is precisely one hierarchy of braces that leads to a sensible notion of higher-order derivations. Thus, the notion of higher-order derivations is independent of human choices. The results of the second part follow from the acyclicity of a certain space of natural operations.