  We identify two Batalin-Vilkovisky algebra structures, one obtained by
Kowalzig and Krahmer on the Hochschild cohomology of an Artin-Schelter regular
algebra with semisimple Nakayama automorphism and the other obtained by Lambre,
Zhou and Zimmermann on the Hochschild cohomology of a Frobenius algebra also
with semisimple Nakayama automorphism, provided that these two algebras are
Koszul dual to each other.
