This paper continues the project, begun in [1], of harmonizing Cartan's classical equivalence method and modern equivariant moving frame a framework dubbed involutive frames. As an attestation fruitfulness our framework, we obtain new, constructive intuitive proof Lie-Tresse theorem (Fundamental basis theorem) first general upper bound on minimal number generating differential invariants for Li...

It is proved that every involutive equivalential equality algebra (E, ∧, ∼, 1), an residualted lattice EQ-algebra, which operation ⊗ defined by x y = (x → 0 ) . Moreover, it showen EQ-algebra we have

Let $nin mathbb{N}$. An additive map $h:Ato B$ between algebras $A$ and $B$ is called $n$-Jordan homomorphism if $h(a^n)=(h(a))^n$ for all $ain A$. We show that every $n$-Jordan homomorphism between commutative Banach algebras is a $n$-ring homomorphism when $n < 8$. For these cases, every involutive $n$-Jordan homomorphism between commutative C-algebras is norm continuous.

In this paper, we consider Rota–Baxter operators on involutive asso-ciative algebras. We define cohomology for involutivealgebras that governs the formal deformation of operator. This cohomologycan be seen as Hochschild a certain associativealgebra with coefficients in suitable bimodule. also relate thiscohomology dendriform Finally, show standard Fard–Guo construction functor from category alg...