let x be a banach space of dimx > 2 and b(x) be the space of bounded linear operators on x. if l : b(x) → b(x) be a lie higher derivation on b(x), then there exists an additive higher derivation d and a linear map τ : b(x) → fi vanishing at commutators [a, b] for all a, b ∈ b(x) such that l = d + τ

Given a ternary relation C on a set U and an algebra A, we present a construction of a convolution algebra A(U,C) of U = (U,C) over A. This generalises bothmatrix algebras and algebras obtained from convolution of monoids. To any class of algebras corresponds a class of convolution structures. Our study cases are the classes of commutative, associative, Lie, and Jordan algebras. In each of thes...

We determine the identities of degree ≤ 6 satisfied by the symmetric (Jordan) product a◦ b = ab+ ba and the associator [a, b, c] = (ab)c−a(bc) in every nonassociative algebra. In addition to the commutative identity a◦b = b◦a we obtain one new identity in degree 4 and another new identity in degree 5. We demonstrate the existence of further new identities in degree 6. These identities define a ...

The title compound, terbium hexa-niobium hexastannide, TbNb(6)Sn(6), is the first ternary compound from the rare earth-niobium-tin system. It has the HfFe(6)Ge(6) structure type, which can be analysed as an inter-growth of the Zr(4)Al(3) and CaCu(5) structures. All the atoms lie on special positions; their coordination geometries and site symmetries are: Tb (dodeca-hedron) 6/mmm; Nb (distorted ...

A number of advantages have been claimed in the recent literature for theories that allow recursive, or internally layered, feet (Bennett 2012, Kager 2012, Martínez-Paricio 2013). The claimed advantages lie in the ability of recursive feet to capture phenomena associated with ternary stress configurations, whether the patterns involve repeating ternary configurations, ternary configurations emb...

In a ternary semihyperring, addition is a hyperoperation and multiplicationis a ternary operation. Indeed, the notion of ternary semihyperringsis a generalization of semirings. Our main purpose of this paper is to introducethe notions of fuzzy hyperideal and fuzzy bi-hyperideal in ternary semihyperrings.We give some characterizations of fuzzy hyperideals and investigateseveral kinds of them.

The theory of crystal bases introduced by Kashiwara in [6] to study the category of integrable representations of quantized Kac–Moody Lie algebras has been a major development in the combinatorial approach to representation theory. In particular Kashiwara defined the tensor product of crystal bases and showed that it corresponded to the tensor product of representations. Later, in [7] he define...

The following integrability theorem for vertex operator algebras V satisfying some finiteness conditions (C2-cofinite and CFT-type) is proved: the vertex operator subalgebra generated by a simple Lie subalgebra g of the weight one subspace V1 is isomorphic to the irreducible highest weight ĝ-module L(k, 0) for a positive integer k, and V is an integrable ĝ-module. The case in which g is replace...

We study the double cosets of a Lie group by a compact Lie subgroup. We show that a Weil formula holds for double coset Lie hypergroups and show that certain representations of the Lie group lift to representations of the double coset Lie hypergroup. We characterize smooth (analytic) vectors of these lifted representations.