We introduce a bicomplex which computes the triple cohomology of Lie– Rinehart algebras. We prove that the triple cohomology is isomorphic to the Rinehart cohomology [13] provided the Lie–Rinehart algebra is projective over the corresponding commutative algebra. As an application we construct a canonical class in the third dimensional cohomology corresponding to an associative algebra.

We prove that, for a Poisson vertex algebra $${\cal V}$$ , the canonical injective homomorphism of variational cohomology to its classical is an isomorphism, provided that viewed as differential algebra, polynomials in finitely many variables. This theorem one key ingredients computation cohomology. For proof, we introduce sesquilinear Hochschild and Harrison complexes vanishing symmetric

| Constraint relational databases use constraints to both model and query data. A constraint relation contains a nite set of generalized tuples. Each generalized tuple is represented by a conjunction of constraints on a given logical theory and, depending on the logical theory and the speciic conjunction of constraints, it may possibly represent an in-nite set of relational tuples. For their ch...

We describe the realizations of finite-dimensional Lie algebras smooth tangential vector fields on a circle and construct “canonical” two-dimensional noncommutative algebra, as well algebra ????????(2,?) . It is shown that any realization these by can be reduced to one with help piecewise-smooth global transformations onto itself. also deduce formulas for number nonequivalent realizations.

This paper briefly reviews the conventional method of obtaining the canonical form of an antisymmetric (skewsymmetric, alternating) matrix. Conventionally a vector space over the complex field has to be introduced. After a short introduction to the universal mathematical “language” Geometric Calculus, its fundamentals, i.e. its “grammar” Geometric Algebra (Clifford Algebra) is explained. This l...

A construction of canonical extensions of Stone algebras is presented that uses the natural duality based on the three-element generating algebra 3 rather than the Priestley duality based on 2 that is traditionally used to build the canonical extension. The new approach has the advantage that the canonical extension so constructed inherits its algebra structure pointwise from a power of the gen...

We find a one parameter family of quadratic Poisson structures on R 4 × SL(2, C) which satisfies the property a) that it is preserved under the Lie-Poisson action of the Lorentz group, as well as b) that it reduces to the standard Poincaré algebra for a particular limiting value of the parameter. (The Lie-Poisson transformations reduce to canonical ones in that limit, which we therefore refer t...

The paper is devoted to concern a relationship between rough set theory and universal algebra. Notions of lower and upper rough approximations on an algebraic structure induced by an ideal are introduced and some of their properties are studied. Also, notions of rough subalgebras and rough ideals with respect to an ideal of an algebraic structure, which is an extended notion of subalgebras and ...

We study a canonical quantization of the Wess{Zumino{Witten (WZW) model which depends on two integer parameters rather than one. The usual theory can be obtained as a contraction, in which our two parameters go to in nity keeping the di erence xed. The quantum theory is equivalent to a generalized Thirring model, with left and right handed fermions transforming under di erent representations of...

This paper is devoted to analyze, inside the ∞-many possible bases of a Quantum Universal Enveloping Algebra Uq(g), those that can be considered as “more equal then others”, like orthonormal bases in the Euclidean spaces. The only possible element of selection has been found to be a privileged connection with the corresponding bialgebra. A new parameter z ∈ C –independent from the z := log(q) ∈...