in this paper we study the concept of ph-biatness ofa banach algebra a, where ph is a continuous homomorphism on a.we prove that if ph is a continuous epimorphism on a and a hasa bounded approximate identity and a is ph- biat, then a is ph-amenable. in the case where ph is an isomorphism on a we showthat the ph- amenability of a implies its ph-biatness.

We give a complete characterization of all indecomposable involutive solutions the Yang-Baxter equation multipermutation level 2. In first step we present construction some family such and in second prove that every solution with 2 is homomorphic image previously constructed. Analyzing this epimorphism, are able to obtain up isomorphism enumerate these small sizes.

We give a systematic construction of epimorphisms between 2–bridge link groups. Moreover, we show that 2–bridge links having such an epimorphism between their link groups are related by a map between the ambient spaces which only have a certain specific kind of singularity. We show applications of these epimorphisms to the character varieties for 2–bridge links and π1 –dominating maps among 3–m...

The non-standard quantum groups CR[GL(⋉)] and CR[SL(⋉)] are constructed for a two parameter version of the Cremmer-Gervais R-matrix. An epimorphism is constructed from CR[GL(⋉)] onto the restricted dual UR̄(gl(n− 1)) associated to a related smaller R-matrix of the same form. A related result is proved concerning factorizable Lie bialgebras. For any such Lie bialgebra, the dual Lie bialgebra has ...

The problem of proving that a given finitely presented group G is infinite can be very difficult (or impossible) in general, but there are several possible approaches that can be tried, some of which can be rendered much more effective with the assistance of computers. To this list, we add another one, which can be applied if an epimorphism of G onto a finite group H is known. The idea depends ...

The mapping class group of a d-pointed Riemann surface has a natural C∞ action on any moduli space of parabolic bundles with the marked points as the parabolic points. We prove that under some numerical conditions on the parabolic data, the induced action of the mapping class group on the cohomology algebra of the moduli space of parabolic bundles factors through the natural epimorphism of the ...

We introduce the notion of operational resolution, i.e., an isotone map from a powerset to a poset that meets two additional conditions, which generalizes the description of states as the atoms in a property lattice (Piron, 1976 and Aerts, 1982) or as the underlying set of a closure operator (Aerts, 1994 and Moore, 1995). We study the structure preservance of the related state transitions and s...

Let S be a closed orientable surface of genus at least two. Let Γ be a Schottky group whose rank is equal to the genus of S, and Ω be the domain of discontinuity of Γ. Pick an arbitrary epimorphism ρ : π1(S) → Γ. Then Ω/Γ is a surface homeomorphic to S carrying a (complex) projective structure with holonomy ρ. We show that every projective structure with holonomy ρ is obtained by (2π-)grafting ...

Main Theorem. For every odd prime power q = p, there is a symmetric design D with parameters (2q+1, q, q 2 −1 2 ) possessing an automorphism group A of order q · ( q−1 2 ) 2 · e · 2 which is isomorphic to the subdirect product of the affine semilinear group AΓL1(q) with itself with respect to a certain epimorphism ψ : AΓL1(q) → Z2 from AΓL1(q) into the cyclic group Z2, i.e. A ∼= AΓL1(q) sdp(ψ,ψ...

In this paper we study the concept of ph-biatness ofa Banach algebra A, where ph is a continuous homomorphism on A.We prove that if ph is a continuous epimorphism on A and A hasa bounded approximate identity and A is ph- biat, then A is ph-amenable. In the case where ph is an isomorphism on A we showthat the ph- amenability of A implies its ph-biatness.