Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the origin of higher braces and higher-order derivations   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.

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The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: cs
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The categories of this paper are: nucl-ex