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Analogous to a recent result of N. Kowalzig and U. Kr\"{a}hmer for twistedCalabi-Yau algebras, we show that the Hochschild cohomology ring of a Frobeniusalgebra with semisimple Nakayama automorphism is a Batalin-Vilkovisky algebra,thus generalizing a result of T.Tradler for finite dimensional symmetricalgebras. We give a criterion to determine when a Frobenius algebra given byquiver with relations has semisimple Nakayama automorphism and apply it to someknown classes of tame Frobenius algebras. We also provide ample examplesincluding quantum complete intersections, finite dimensional Hopf algebrasdefined over an algebraically closed field of characteristic zero and Koszulduals of Koszul Artin-Schelter regular algebras of dimension three.

The Hochschild cohomology ring of a Frobenius algebra with semisimple Nakayama automorphism is a Batalin-Vilkovisky algebra