Consider a Poisson structure on C∞(R3,R) with bracket {, } and suppose that C is a Casimir function. Then {f, g} =< ∇C, (∇g × ∇f) > is a possible Poisson structure. This confirms earlier observations concerning the Poisson structure for Hamiltonian systems that are reduced to a one degree of freedom system and generalizes the Lie-Poisson structure on the dual of a Lie algebra and the KKS-symple...

in this paper, we consider a class of connected oriented (with respect to z/p) closed g-manifolds with a non-empty finite fixed point set, each of which is g-equivariantly formal, where g = z/p and p is an odd prime. using localization theorem and equivariant index, we give an explicit description of the mod p equivariant cohomology ring of such a g-manifold in terms of algebra. this makes it p...

Every continuous map X → S defines, by composition, a homomorphism between the corresponding algebras of real-valued continuous functions C(S) → C(X). This paper deals with algebraic properties of the homomorphism C(S)→ C(X) in relation to topological properties of the map X → S. The main result of the paper states that a continuous map X → S between topological manifolds is a finite (branched)...

Let α be a polynomial Poisson bivector on a finite-dimensional vector space V over C. Then Kontsevich [K97] gives a formula for a quantization f ⋆ g of the algebra S(V )∗. We give a construction of an algebra with the PBW property defined from α by generators and relations. Namely, we define an algebra as the quotient of the free tensor algebra T (V ∗) by relations xi ⊗ xj − xj ⊗ xi = Rij(~) wh...

Contents 1. Introduction 1 2. Carlitz-Fermat quotients 2 3. Non-vanishing of Carlitz-Fermat quotients modulo primes 4 1. Introduction. Let q = p s , where p is a prime and s is a positive integer. Let F q be the finite field of q elements, and set A = F q [T ] and k = F q (T). Let τ be the mapping defined by τ (x) = x q , and let kτ denote the twisted polynomial ring. Let C : A → kτ (a → C a) b...

We describe a finite analogue of the Poisson Algebra of Wilson Loops in Yang–Mills theory. It is shown that this algebra arises in an apparently completely different context: as a Lie algebra of vector fields on a non–commutative space. This suggests that non–commutative geometry plays a fundamental role in the manifestly gauge invariant formulation of Yang–Mills theory. We also construct the d...

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...

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 $e$.