‎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...

The notion of vertex operator algebra ([B], [FHL], [FLM]) is the algebraic counterpart of the notion of what is now usually called “chiral algebra” in conformal field theory, and vertex operator algebra theory generalizes the theories of affine Lie algebras, the Virasoro algebra and representations (cf. [B], [DL], [FLM], [FZ]). It has been well known (cf. [FZ], [L1]) that the irreducible highes...

‎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...

In this paper, we investigate more relations between the symmetric residuated lattices $L$ with their corresponding intuitionistic fuzzy residuated lattice $tilde{L}$. It is shown that some algebraic structures of $L$ such as Heyting algebra, Glivenko residuated lattice and strict residuated lattice are preserved for $tilde{L}$. Examples are given for those structures that do not remain the sam...

It is shown that $A:=H_{1,\eta}(G)$, the Sympectic Reflection Algebra, has $T_G$ independent traces, where number of conjugacy classes elements without eigenvalue 1 belonging to finite group $G$ generated by system symplectic reflections. Simultaneously, we show algebra $A$, considered as a superalgebra with natural parity, $S_G$ supertraces, -1 $G$. We consider also $A$ Lie $A^L$ and $A^S$. if...

In this paper, first we study the semi maximal filters in linear $BL$-algebras and we prove that any semi maximal filter is a primary filter. Then, we investigate the radical of semi maximal filters in $BL$-algebras. Moreover, we determine the relationship between this filters and other types of filters in $BL$-algebras and G"{o} del algebra. Specially, we prove that in a G"{o}del algebra, any ...

Consider a Lie color algebra, denoted by L. Our aim in this paper is to study the triple derivations TDer(L) and generalized GTDer(L) of algebras. We discuss centroids, quasi centroids central algebras, where we show relationship derivation with algebras A classification algebra all perfect given, prove that for centerless TDer(L)=Der(L) TDer(Der(L))=Inn(Der(L)).

A Lie bialgebra is a vector space endowed simultaneously with the structure of algebra and coalgebra, some compatibility condition. Moreover, brackets have skew symmetry. Because close relation between bialgebras quantum groups, it interesting to consider structures on L related Virasoro algebra. In this paper, are investigated by computing Der(L, L⊗L). It proved that all such triangular coboun...

Dragan Mašulović Abstract. One can turn the set of retractions of a lattice 〈L,≤〉 into a poset Rf (L) by letting f ≤ g iff f(x) ≤ g(x) for all x ∈ L. In 1982 H. Crapo raised the following two problems: (1) Is it true that Rf (L) is a lattice for any lattice L? (2) Is it true that Rf (L) is a complete lattice if L is a complete lattice? In 1990 and 1991 B. Li published two papers dealing with th...