The fundamental tool in the classification of orthogonal coordinate systems in which the Hamilton–Jacobi and other prominent equations can be solved by a separation of variables are second order Killing tensors which satisfy the Nijenhuis integrability conditions. The latter are a system of three non-linear partial differential equations. We give a simple and completely algebraic proof that for...

In this brief note we would like to give the construction of a free commutative unital associative Nijenhuis algebra on a commutative unital associative algebra based on an augmented modified quasi-shuffle product. —————————————

In this note I exhibit a “discrete homotopy” which joins the category of Fmanifolds to the category of Poisson–Nijenhuis manifolds, passing through the category of Frobenius manifolds.

In this paper we construct an L∞ structure on polyvector fields on a vector space V over C where V may be infinite-dimensional. We prove that the constructed L∞ algebra of polyvector fields is L∞ equivalent to the Hochschild complex of polynomial functions on V , even in the infinite-dimensional case. For a finite-dimensional space V , our L∞ algebra is equivalent to the classical Schouten-Nije...

Abstract We give the description of Rota–Baxter operators, Reynolds Nijenhuis operators and average on 3-dimensional nilpotent associative algebras over ℂ.

We discuss the diagonalization problem of Nijenhuis tensor in a class Poisson-Nijenhuis structures defined on compact hermitian symmetric spaces. study its action ring invariant polynomials Thimm chain subalgebras. The existence $\phi$-minimal representations defines suitable basis that completely solves problem. prove such exist classical cases AIII, BDI, DIII and CI, do not exceptional EIII E...

Gauge theory usually investigates the space of principal connections on a principal fiber bundle (P, p, M, G) and its orbit space under the action of the gauge group (called the moduli space), which is the group of all principal bundle automorphisms of P which cover the identity on the base space M. It is the arena for the Yang-Mills-Higgs equations which allows (with structure group U (1) × SU...