Let CRF S denote the category of S-colored rooted forests, and HCRFS denote its Ringel-Hall algebra as introduced in [6]. We construct a homomorphism from a K+ 0 (CRF S)–graded version of the Hopf algebra of noncommutative symmetric functions to HCRFS . Dualizing, we obtain a homomorphism from the Connes-Kreimer Hopf algebra to a K+ 0 (CRF S)–graded version of the algebra of quasisymmetric func...

in this article, the notion of $n-$derivation is introduced for all integers $ngeq 2$. although all derivations are $n-$derivations,  in general these notions are not equivalent. some properties of ordinary derivations are  investigated for $n-$derivations. also, we show that under certain mild condition  $n-$derivations are derivations.

We prove that a discrete group G is amenable iff it is strongly unitarizable in the following sense: every unitarizable representation π on G can be unitarized by an invertible chosen in the von Neumann algebra generated by the range of π. Analogously a C *-algebra A is nuclear iff any bounded homomorphism u : A → B(H) is strongly similar to a *-homomorphism in the sense that there is an invert...

We give a structure theorem for a ring homomorphism of a commutative regular Banach algebra into another commutative Banach algebra. In particular, it is shown that: (i) A ring homomorphism of a commutative C∗-algebra onto another commutative C∗-algebra with connected infinite Gelfand space is either linear or anti-linear. (ii) A ring automorphism of L1(R ) is either linear or anti-linear. (iii...

using the hyers-ulam-rassias stability method, weinvestigate isomorphisms in banach algebras and derivations onbanach algebras associated with the following generalized additivefunctional inequalitybegin{eqnarray}|af(x)+bf(y)+cf(z)|  le  |f(alpha x+ beta y+gamma z)| .end{eqnarray}moreover, we prove the hyers-ulam-rassias stability of homomorphismsin banach algebras and of derivations on banach ...

The algebra Ψ(M) of order zero pseudodifferential operators on a compact manifold M defines a well-known C∗-extension of the algebra C(S∗M) of continuous functions on the cospherical bundle S∗M ⊂ T ∗M by the algebra K of compact operators. In his proof of the index theorem, Higson defined and used an asymptotic homomorphism T from C0(T ∗M) to K, which plays the role of a deformation for the com...

We show that the algebra homomorphism Uq(ĝln) ։ K GLd×C ∗ (Z)⊗C(q) constructed by Ginzburg and Vasserot between the quantum affine algebra of type gln and the equivariant K-theory group of the Steinberg variety (of incomplete flags), specializes to a surjective homomorphism U res ǫ (ĝln) ։ K GLd×C ∗ ǫ (Z). In particular, this shows that the parametrization of irreducible U res ǫ (ŝln)-modules a...

We show a relation of the KMS state of a certain C∗Algebra U with the Gibbs state of Thermodynamic Formalism. More precisely, we consider here the shift T : X → X acting on the Bernoulli space X = {1, 2, ..., k} and μ a Gibbs state defined by a Holder continuous potential p : X → R, and L(μ) the associated Hilbert space. Consider the C∗-Algebra U = U(μ), which is a sub-C∗-Algebra of the C∗-Alge...

We define a nontrivial homomorphism from the Hecke algebra of type B onto a reduced algebra of the Hecke algebra of type A at roots of unity. We use this homomorphism to describe semisimple quotients of the Hecke algebra of type B at roots of unity. Using these quotients we determine subfactors obtained from the inclusion of Hecke algebra of type A into Hecke algebras of type B. We also study i...

We consider the double affine Hecke algebra H = H(k0, k1, k∨ 0 , k ∨ 1 ; q) associated with the root system (C∨ 1 , C1). We display three elements x, y, z in H that satisfy essentially the Z3-symmetric Askey–Wilson relations. We obtain the relations as follows. We work with an algebra Ĥ that is more general than H, called the universal double affine Hecke algebra of type (C∨ 1 , C1). An advanta...