Integrating L∞-algebras

Integrating L∞-algebras

Similarity DH-Algebras

In  cite{GL}, B. Gerla and I. Leuc{s}tean introduced the notion of similarity on MV-algebra. A similarity MV-algebra is an MV-algebra endowed with a binary operation $S$ that verifies certain additional properties. Also, Chirtec{s} in cite{C}, study the notion of similarity on L ukasiewicz-Moisil algebras. In particular, strong similarity L ukasiewicz-Moisil algebras were defined. In this paper...

The structure of a pair of nilpotent Lie algebras

Assume that $(N,L)$, is a pair of finite dimensional nilpotent Lie algebras, in which $L$ is non-abelian and $N$ is an ideal in $L$ and also $mathcal{M}(N,L)$ is the Schur multiplier of the pair $(N,L)$. Motivated by characterization of the pairs $(N,L)$ of finite dimensional nilpotent Lie algebras by their Schur multipliers (Arabyani, et al. 2014) we prove some properties of a pair of nilpoten...

On dimension of a special subalgebra of derivations of nilpotent Lie algebras

‎Let $L$ be a Lie algebra‎, ‎$mathrm{Der}(L)$ be the set of all derivations of $L$ and $mathrm{Der}_c(L)$ denote the set of all derivations $alphainmathrm{Der}(L)$ for which $alpha(x)in [x,L]:={[x,y]vert yin L}$ for all $xin L$‎. ‎We obtain an upper bound for dimension of $mathrm{Der}_c(L)$ of the finite dimensional nilpotent Lie algebra $L$ over algebraically closed fields‎. ‎Also‎, ‎we classi...

Module-Amenability on Module Extension Banach Algebras

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...

First Order Cohomology of l^1-Munn Algebras and Certain Semigroup Algebras