In this paper we introduce a general construction which as~ sociate~ an algebra A(e,b)with every pair (e,b~ where e is a Lie algebra and b is an invariant symmetric bilinear form on e. By virtue of this construction several well-known (as­ sociative and non-associative)algebras can be dealt with un­ der a unified view. We give characterizations of ,those pairs (e,b)which generate associative al...

It is well known that any Lie algebra can be embedded into an associative algebra. We prove metabelian in the subvariety of perm algebras, i.e. algebras with identity [Formula: see text]. In addition, a technical method to construct universal enveloping for given.

We give a definition and study Hopf structures in ternary ( and n-ary) NambuLie algebra. The fundamental concepts of 3-coalgebra, 3-bialgebra and Hopf 3algebra are introduced. Some examples of Hopf structures are analyzed. Mathematics Subject Classification (1991) 70H99, 58F07 1 [email protected] 2 [email protected] In 1973 Yoishira Nambu [1] proposed a generalization of classical Hamiltonian mecha...

We fuzzify the concept of an associative -ideal in an IS-algebra. We give a relation between a fuzzy -ideal and a fuzzy associative -ideal, and we investigate some related properties.

Abstract. For an (ǫ,Γ)-color-commutative associative algebra A with an identity element over a field F of characteristic not 2, and for a color-commutative subalgebraD of color-derivations of A, denote by A[D] the associative subalgebra of End(A) generated by A (regarding as operators on A via left multiplication) and D. It is easily proved that, as an associative algebra, A[D] is Γgraded simpl...

We consider an evolution algebra which corresponds to a bisexual population with a set of females partitioned into finitely many different types and the males having only one type. For such algebras in terms of its structure constants we calculate right and plenary periods of generator elements. Some results on subalgebras of EACP and ideals on low-dimensional EACP are obtained.

shuffle product of the permutations u E E k and v' E E k, we mean the following element from ~+~, /,, (i), i < k , vmv'=: Z o'o(~,| where (v~v') ( i ) = ~ . v , ( i _ k ) + l e ' i ' > k . a(~sk+n'cn} Since the permutations form an additive basis of the space ~ , the shuffle multiplication is uniquely extended "by linearity" to any pair of elements from ~ and defines in $ = ~0$n a structure of ...

We define a generalization of Massey products for algebras over Koszul operad in characteristic zero, extending Massey’s and Allday’s Retah’s the associative Lie cases, respectively. establish connections with minimal models Dimitrova’s universal operadic cohomology class. compute Gerstenhaber algebra example hypercommutative related to Chevalley–Eilenberg complex Heisenberg algebra.

Associated with any oligomorphic permutation group G there is a graded algebra A such that the dimension of its nth homogeneous component is equal to the number of G orbits on n sets I show that the algebra is a poly nomial algebra free commutative associative algebra in some cases and pose some questions about transitive extensions