Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A rigidity theorem for preLie algebras   In this paper we prove a ``Leray theorem'' for preLie algebras. We define a
notion of ''Hopf'' preLie algebra: it is a preLie algebra together with a non
associative permutative coproduct D and a compatibility relation between the
preLie product and the coproduct D. A nonassociative permutative algebra is a
vector space together with a product satisfying the relation (ab)c=(ac)b. A non
associative permutative coalgebra is the dual notion. We prove that any such
graded connected "Hopf" preLie algebra is a free preLie algebra. It uses the
description of preLie algebras in term of rooted trees developped by Chapoton
and the author. We interpret also this theorem by way of cogroups in the
category of preLie algebras.

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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con
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The categories of this paper are: cs
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: physics