In this paper, first we show that the invariant bilinear form in a quadratic Lie-Yamaguti algebra induces an isomorphism between adjoint representation and coadjoint representation. Then introduce notions of relative Rota-Baxter operators on algebras pre-Lie-Yamaguti algebras. We prove gives rise to naturally operator algebra. Finally, study symplectic structures algebra, which give as well As ...

The essential parts of the operad algebra are concisely presented, which should be useful when confronting with the operadic physics. It is also clarified how the Gerstenhaber algebras can be associated with the linear pre-operads (comp algebras). Their relation to mechanics is concisely discussed.

In [2] we investigated the lattice Λ(Df2) of all subvarieties of the variety Df2 of two-dimensional diagonal free cylindric algebras. In the present paper we investigate the lattice Λ(CA2) of all subvarieties of the variety CA2 of two-dimensional cylindric algebras. We give a dual characterization of representable two-dimensional cylindric algebras, prove that the cardinality of Λ(CA2) is that ...

Description of the pairs 〈low approximation, upper approximation〉 of rough sets is an important aspect in the research of rough set theory by algebraic method. By defining some basic operators on the approximation pairs, rough algebras can be constructed. Then some general algebras can be selected to describe the pairs of rough sets. The most famous rough algebras are Rough Double Stone Algebra...

We give an account of fundamental properties of pre-Lie algebras, and provide several examples borrowed from various domains of Mathematics and Physics : Algebra, Combinatorics, Quantum Field Theory and Numerical Analysis.

We study topological von Neumann regularity and principal von Neumann regularity of Banach algebras. Our main objective is comparing these two types of Banach algebras and some other known Banach algebras with one another. In particular, we show that the class of topologically von Neumann regular Banach algebras contains all $C^*$-algebras, group algebras of compact abelian groups and ...

A field of endomorphisms R is called a Nijenhuis operator if its torsion vanishes. In this work we study specific kind singular points scalar type. We show that the tangent space at such possesses natural structure left-symmetric algebra (also known as pre-Lie or Vinberg-Kozul algebras). Following Weinstein's approach to linearization Poisson structures, state linearisation problem for operator...

In this paper, first we introduce the notion of a Reynolds operator on an n-Lie algebra and illustrate relationship between operators derivations algebra. We give cohomology theory study infinitesimal deformations using second group. Then NS-n-Lie algebras, which are generalizations both algebras n-pre-Lie algebras. show that gives rise to together with representation itself. Nijenhuis naturall...

We introduce the categories of infinitesimal Hopf modules and bimodules over an infinitesimal bialgebra. We show that they correspond to modules and bimodules over the infinitesimal version of the double. We show that there is a natural, but non-obvious way to construct a pre-Lie algebra from an arbitrary infinitesimal bialgebra and a dendriform algebra from a quasitriangular infinitesimal bial...

In this paper we study particular classes of pseudo-BCK algebras, bounded or not bounded, as pseudo-BCK(pP) algebras, pseudo-BCK(pP) lattices, pseudo-Hájek(pP) algebras and pseudo-Wajsberg algebras. We introduce new classes of pseudo-BCK(pP) lattices, we establish hierarchies and we give some examples. We work with left-defined algebras and we work with → and ; as primitive operations, not with...