Semi-symmetric algebras: General constructions

Algebras from Standard Constructions

Constructions of Dgbv Algebras from Lie Algebras

We give some constructions of diierential Gerstenhaber-Batalin-Vilkovisky algebras from a class of Lie algebras. In our construction, we make use of the solutions to the classical Yang-Baxter equations, and ideas from Poisson geometry. A graded commutative algebra (A; ^) with a bracket ] of degree?1 is called a G-algebra (Gerstenhaber algebra) if: (a) (A1]; ]) is a Lie algebra, where A1] is A w...

Tensor Algebras, Symmetric Algebras and Exterior Algebras

We begin by defining tensor products of vector spaces over a field and then we investigate some basic properties of these tensors, in particular the existence of bases and duality. After this, we investigate special kinds of tensors, namely, symmetric tensors and skew-symmetric tensors. Tensor products of modules over a commutative ring with identity will be discussed very briefly. They show up...

On (Semi)Topological $BL$-algebras

In last ten years many mathematicians have studied properties of BL-algebras endowed with a topology. For example A. Di Nola and L. Leustean cite{dn} studied compact representations of BL-algebras, L. C. Ciungu cite{ciu} investigated some concepts of convergence in the class of perfect BL-algebras, J. Mi Ko and Y. C. Kim cite{jun} studied relationships between closure operators and BL-algebras,...

Dynamic algebras: Examples, constructions, applications

Dynamic algebras combine the classes of Boolean (B ∨ ′ 0) and regular (R ∪ ; ∗) algebras into a single finitely axiomatized variety (B R 3) resembling an R-module with “scalar” multiplication 3. The basic result is that ∗ is reflexive transitive closure, contrary to the intuition that this concept should require quantifiers for its definition. Using this result we give several examples of dynam...