We study a two-boundary extension of the Temperley-Lieb algebra which has recently arisen in statistical mechanics. This algebra lies in a quotient of the affine Hecke algebra of type C and has a natural diagrammatic representation. The algebra has three parameters and, for generic values of these, we determine its representation theory. We use the action of the centre of the affine Hecke algeb...

Let H be a finite-dimensional quasi-Hopf algebra. We show for each quotient quasibialgebra Q of H that Q is a quasi-Hopf algebra whose dimension divides the dimension of H.

We prove that the non-CM Q-abelian surfaces whose endomorphism algebra is a quaternion algebra are parametrized, up to isogeny, by the rational points of the quotient of certain Shimura curves by the group of their Atkin-Lehner involutions.

We provide a necessary and sufficient condition for type D Temperley-Lieb algebra TLDn(δ) being semi-simple by studying branching rule cell modules. As byproduct, our result is used to study the so-called forked algebra, which quotient of TLDn(δ).

We build, using the notion of zinbiel algebra, some commutative subalgebras C_{u,v} inside an algebra formal iterated integrals. There is a quotient map from this integrals to motivic multiple zeta values. Restricting gives morphism graded algebras with same dimension. This conjectured be generically isomorphism. When u+v = 0, image instead sub-algebra

In this paper we study the relationships among the spectra of the cosets of an element of a Banach algebra in some quotient algebras. We also characterize the spectrum of any a E M (where M is an ideal of a Banach algebra with identity and moreover has an identity) in the whole algebra in terms of the spectrum of a in M.