This paper provides a general operadic definition for the notion of splitting operations algebraic structures. construction is proved to be equivalent some Manin products operads and it shown closely related Rota-Baxter operators. Hence, gives new effective way compute black products. The present have symmetry properties. Finally, this allows us describe structure square matrices with coefficients in algebras certain types. Many examples illustrate text, including case Jordan algebras.

Let f be a newform of weight k⩾2, level N with coefficients in number field K, and A the adjoint motive M associated to f. We carefully discuss construction realisations A, as well natural integral structures these realisations. then use method Taylor Wiles verify λ-part Tamagawa conjecture Bloch Kato for L(A,0) L(A,1). Here λ is any prime K not dividing Nk!, so that mod representation absolutely irreducible when restricted Galois group over Q((−1)(ℓ−1)/2ℓ) where λ|ℓ. The also establishes...

In this paper we continue to explore the notion of Rota–Baxter algebras in context Hopf algebraic approach renormalization theory perturbative quantum field theory. We show very simple terms that solutions recursively defined formulae for Birkhoff factorization regularized algebra characters, i.e. Feynman rules, naturally give a non-commutative generalization well-known Spitzer's identity. The underlying abstract structure is analysed complete filtered algebras.

This paper studies two types of 3-Lie bialgebras whose compatibility conditions between the multiplication and comultiplication are given by local cocycles double constructions respectively, therefore called cocycle bialgebra construction bialgebra. They can be regarded as suitable extensions well-known Lie in context algebras, different directions. The is introduced to extend connection classical Yang-Baxter equation. Its relationship with a ternary variation equation,...

Scholars have begun to realize the importance of entrepreneurial political skills new ventures. Namely, social entrepreneurship is a context, in which entrepreneurs expend great efforts networking politically integrate diverse resources and share interests (e.g., ecology wellness) for sustainability. In this paper, we exchange theory resource-based view discuss how entrepreneurs' enhance ventures' performance through their network (size/diversity structural holes), psychological capital...

A Rota–Baxter algebra, also known as a Baxter is an algebra with linear operator satisfying relation, called the that generalizes integration by parts formula. Most of studies on algebras have been for commutative algebras. Two constructions free were obtained Rota and Cartier in 1970s third one Keigher authors 1990s terms mixable shuffles. Recently, noncommutative appeared both physics connection work Connes Kreimer renormalization perturbative quantum field theory, mathematics related to...

An ᏻ-operator on an associative algebra is a generalization of Rota-Baxter operator that plays important role in the Hopf approach Connes and Kreimer to renormalization quantum field theory.It also analog Lie study classical Yang-Baxter equation.We introduce concept extended whose has been applied generalized Lax pairs PostLie algebras.We algebraic structures coming from ᏻ-operators.Continuing work Aguiar deriving operators equation, we show its solutions correspond ᏻ-operators through...