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

Let A be a Banach algebra. We call a pair (G,A) a Gelfand theory for A if the following axioms are satisfied: (G 1) A is a C∗-algebra, and G : A → A is a homomorphism; (G 2) the assignment L 7→ G−1(L) is a bijection between the sets of maximal modular left ideals of A and A, respectively; (G 3) for each maximal modular left ideal L of A, the linear map GL : A/G−1(L) → A/L induced by G has dense...

20.1 Classical Hamiltonian Reduction of a Poisson Vertex Algebra Let V be a Poisson vertex algebra, and suppose we are given a triple (V0, I0, φ) where V0 is a Poisson vertex algebra, I0 ⊂ V0 is a Poisson vertex algebra ideal, and φ : V0 → V is a Poisson vertex algebra homomorphism. Then the Hamiltonian reduction associated to (V0, I0, φ) is the differential algebra W =W(V0, I0, φ) := (V/Vφ(I0)...

4 Conjectures and results 12 4.1 The symmetry conjecture . . . . . . . . . . . . . . . . . . . . . . 12 4.2 Othogonal idempotents and character formulas . . . . . . . . . . 15 4.3 The double coset conjecture . . . . . . . . . . . . . . . . . . . . . 17 4.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 4.5 The case of a single generator . . . . . . . . . . . . . . ...

let $a$ be a $c^*$-algebra and $e$ be a left hilbert $a$-module. in this paper we define a product on $e$ that making it into a banach algebra and show that under the certain conditions $e$  is arens regular. we also study the relationship between derivations of $a$ and $e$.

Notes taken by Stuart White during the lectures and not proof read. Errors will abound. 1. Nuclearity: Approximation and perturbation Recall: Definition 1.1. A C∗-algebra. Definition 1.2. A cp map Theorem 1.3. Stinespring’s theorem. Every cp map is a compression of a ∗-homomorphism. Definition 1.4. φ : A → B cp has order zero if a ⊥ b =⇒ φ(a) ⊥ φ(b). 1 Theorem 1.5. (i) φ : A→ B has order zero i...

The descent algebra of the symmetric group, over a field of non-zero characteristic p, is studied. A homomorphism into the algebra of generalised p-modular characters of the symmetric group is defined. This is then used to determine the radical, and its nilpotency index. It also allows the irreducible representations of the descent algebra to be described.

In this article, it is proved that under some conditions every bijective Jordan triple product homomorphism from generalized matrix algebras onto rings is additive. As a corollary, we obtain that every bijective Jordan triple product homomorphism from Mn(A) (A is not necessarily a prime algebra) onto an arbitrary ring R is additive.

However it can just as well be considered a fundamental representation theorem of universal algebra, via the connection between the homfunctor of a category and free algebras for the theory represented by that category. This connection is not generally appreciated outside category theoretic circles, which this section endeavors to correct by presenting the relevant concepts from an algebraic pe...