Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Natural endomorphisms of shuffle algebras   We focus in this text on the adaptation to the study of shuffles of the main
combinatorial tool in the theory of free Lie algebras, namely the existence of
a universal algebra of endomorphisms for tensor and other cocommutative Hopf
algebras: the family of Solomon's descent algebras of type A. We show that
there exists similarly a natural endomorphism algebra for commutative shuffle
algebras, which is a natural extension of the Malvenuto-Reutenauer Hopf algebra
of permutations, or algebra of free quasi-symmetric functions. We study this
new algebra for its own, establish freeness properties, study its generators,
bases, and also feature its relations to the internal structure of shuffle
algebras.

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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: stat
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-ex