Abstract We introduce a construction that produces from each bialgebra H an operad $$\mathsf {Ass}_H$$ Ass H controlling associative algebras in the monoidal category of -modules or, briefly, -algebras. When underlying algebra this is Koszul, we give explicit formulas f...

We obtain the bi-Hamiltonian structure of the super KP hierarchy based on the even super KP operator Λ = θ + ∑∞ i=−2 Uiθ , as a supersymmetric extension of the ordinary KP bi-Hamiltonian structure. It is expected to give rise to a universal super W -algebra incorporating all known extended superconformal WN algebras by reduction. We also construct the super BKP hierarchy by imposing a set of an...

Here, we investigate symmetric bi-derivations and their generalizations on L? 0 (G)*. For k ? N, show that if B:L?0(G)*x L?0(G)* is asymmetric bi-derivation such [B(m,m),mk] Z(L?0(G)*) for all m (G)*, then B the zero map. Furthermore, characterize generalized biderivations group algebras. We also prove any Jordan 0(G)* a bi-derivation.