Handle element on nearly Frobenius algebras

In this paper, the concept of handle element of Frobenius algebras, as in Kock [Frobenius Algebras and 2-D Topological Quantum Field Theories (Cambridge University Press, Cambridge, 2004)], will be extended to nearly Frobenius algebras. The main properties of this element will be analyzed in this case and many examples will be constructed. Also, the Casimir and Schur elements of symmetric algebras will be considered [Broué, Michigan Math. J.58 (2009) 125–179] and generalized for Frobenius and nearly Frobenius algebras showing which results still hold in this framework and which ones fail.