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PRE-NAP AND POST-NAP ALGEBRAS
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We introduce and study two new classes of algebraic structures: pre-NAP algebras andpost-NAP algebras, which arise naturally as decompositions of the NAP (non-associative permutative) product. A pre-NAP algebra is a vector space equipped with two binary operations whose sum is a NAP product. A post-NAP algebra extends this structure with a third operation satisfying additional compatibility conditions. We give examples related to shuffles and quasi-shuffles products. We also construct pre-NAP and post-NAP algebras from Rota-Baxter and Reynolds operators.
Title: PRE-NAP AND POST-NAP ALGEBRAS
Description:
We introduce and study two new classes of algebraic structures: pre-NAP algebras andpost-NAP algebras, which arise naturally as decompositions of the NAP (non-associative permutative) product.
A pre-NAP algebra is a vector space equipped with two binary operations whose sum is a NAP product.
A post-NAP algebra extends this structure with a third operation satisfying additional compatibility conditions.
We give examples related to shuffles and quasi-shuffles products.
We also construct pre-NAP and post-NAP algebras from Rota-Baxter and Reynolds operators.
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