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PBW property for associative universal enveloping algebras over an operad

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 نشر من قبل Anton Khoroshkin
 تاريخ النشر 2018
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 تأليف Anton Khoroshkin




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Given a symmetric operad $mathcal{P}$ and a $mathcal{P}$-algebra $V$, the associative universal enveloping algebra ${mathsf{U}_{mathcal{P}}}$ is an associative algebra whose category of modules is isomorphic to the abelian category of $V$-modules. We study the notion of PBW property for universal enveloping algebras over an operad. In case $mathcal{P}$ is Koszul a criterion for the PBW property is found. A necessary condition on the Hilbert series for $mathcal{P}$ is discovered. Moreover, given any symmetric operad $mathcal{P}$, together with a Grobner basis $G$, a condition is given in terms of the structure of the underlying trees associated with leading monomials of $G$, sufficient for the PBW property to hold. Examples are provided.



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