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Homotopy DG algebras induce homotopy BV algebras

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John Terilla, Thomas Tradler and Scott O. Wilson

Let $TA$ denote the space underlying the tensor algebra of a vector space $A$.
In this short note, we show that if $A$ is a differential graded algebra,
then $TA$ is a differential Batalin-Vilkovisky algebra. Moreover, if $A$
is an $A_\infty$ algebra, then $TA$ is a commutative $BV_\infty$ algebra.

Journal of Homotopy and Related Structures, Vol. 6(2011), No. 1, pp. 177-182