Tensor products and perturbations of BiHom-Novikov-Poisson algebras (Q2223750)

A Novikov-Poisson algebra is given an associative product \(\cdot\) and a pre-Lie product \(*\), with the complementary axioms \[ x*(y*z)=(x*z)*y, \] \[ (x*y)\cdot z-x*(y\cdot z)=(y*x)\cdot z-y*(x\cdot z), \] \[ (x\cdot y)*z=(x*z)\cdot y. \] A biHom Novikov-Poisson algebra is a Novikov-Poisson algebra with two twocommuting algebra endomorphisms, satisfying complementary conditions of compatibilities with the products \(\cdot\) and \(*\). In this paper, a structure of biHom Novikov-Poisson algebra on the tensor product of two biHom Novikov-Poisson algebras. Moreover, it is shown that these objects can de deformed according to certain of their elements, generalizing a result due to Xu in the classical case and to Yau in the Hom case. Finally, a classe of biHom Novikov-Poisson algebras is introduced, which gives rise to biHom Poisson algebras. It is shown that this class is preserved under the tensor product, the Yau twist and the deformations mentioned above.