Let $A$ be a Banach algebra and $E$ be a Banach $A$-bimodule then $S = A oplus E$, the $l^1$-direct sum of $A$ and $E$ becomes a module extension Banach algebra when equipped with the algebras product $(a,x).(a^prime,x^prime)= (aa^prime, a.x^prime+ x.a^prime)$. In this paper, we investigate $triangle$-amenability for these Banach algebras and we show that for discrete inverse semigroup $S$ with...

We show that a graded commutative algebra A with any square zero odd differential operator is a natural generalization of the Batalin–Vilkovisky algebra. While such an operator of order 2 defines a Lie algebra structure on A, an operator of an order higher than 2 (Koszul–Akman definition) leads to the structure of a strongly homotopy Lie algebra (L∞–algebra) on A. This allows us to give a defin...

The (real) GraviGUT algebra is an extension of the spin(11, 3) algebra by a 64dimensional Lie algebra, but there is some ambiguity in the literature about its definition. Recently, Lisi constructed an embedding of the GraviGUT algebra into the quaternionic real form of E8. We clarify the definition, showing that there is only one possibility, and then prove that the GraviGUT algebra cannot be e...

the concept of soft sets, introduced by molodtsov [20] is a mathematicaltool for dealing with uncertainties, that is free from the difficultiesthat have troubled the traditional theoretical approaches. in this paper, weapply the notion of the soft sets of molodtsov to the theory of hilbert algebras.the notion of soft hilbert (abysmal and deductive) algebras, soft subalgebras,soft abysms and sof...

let $mathfrak{l}$ be the virasoro-like algebra and $mathfrak{g}$ itsderived algebra, respectively. we investigate the structure of the lie triplederivation algebra of $mathfrak{l}$ and $mathfrak{g}$. we provethat they are both isomorphic to $mathfrak{l}$, which provides twoexamples of invariance under triple derivation.

in this paper, we show that every surjective $n$-homomorphism ($n$-anti-homomorphism) from a banach algebra $a$ into a semisimple banach algebra $b$ is continuous.

in [1,2,3], a. c. baker and j.w. baker studied the subspace ma(s) of the convolution measure algebra m, (s) of a locally compact semigroup. h. dzinotyiweyi in [5,7] considers an analogous measure space on a large class of c-distinguished topological semigroups containing all completely regular topological semigroups. in this paper, we extend the definitions to study the weighted semigroup algeb...

We prove that an associative algebra A is isomorphic to a subalgebra of a C∗-algebra if and only if its ∗-double A∗A∗ is ∗-isomorphic to a ∗-subalgebra of a C∗-algebra. In particular each operator algebra is shown to be completely boundedly isomorphic to an operator algebra B with the greatest C∗-subalgebra consisting of the multiples of the unit and such that each element in B is determined by...

The article concerns the subalgebra U v (w) of the quantized universal enveloping algebra of the complex Lie algebra sln+1 associated with a particular Weyl group element of length 2n. We verify that U v (w) can be endowed with the structure of a quantum cluster algebra of type An. The quantum cluster algebra is a deformation of the ordinary cluster algebra Geiß-Leclerc-Schröer attached to w us...

In this paper, we study and analyze the algebraic structure of the circular cone. We establish a new efficient spectral decomposition, set up the Jordan algebra associated with the circular cone, and prove that this algebra forms a Euclidean Jordan algebra with a certain inner product. We then show that the cone of squares of this Euclidean Jordan algebra is indeed the circular cone itself. The...