Extended zigzag Schur algebras are quasi-hereditary which conjecturally Morita equivalent to RoCK blocks of classical algebras. We prove that extended Ringel self-dual.

Let C denote the algebra of functions continuous on the unit circle. With norm ||/¡| =sup¡xi-i \f(X)\, C is a Banach algebra. Let A denote the set of all / in C which are boundary values of functions analytic in \z\ <1 and continuous in \z\ ál. A is then a closed subalgebra of C, and by known results A consists of those and only those/ in C for which /|X|-l/(X)XBdX = 0, «^0. In [l ] the questio...

J. Németh has extended several basic theorems of R. P. Boas Jr. pertaining to Fourier series with positive coefficients from Lipschitz classes to generalized Lipschitz classes. The goal of the present work is to find the common root of known results of this type and to establish two theorems that are generalizations of Németh’s results. Our results can be considered as sample examples showing t...

Inspired by [3] we introduce the concept of extended Hopf algebra and consider their cyclic cohomology in the spirit of Connes-Moscovici [3, 4, 5]. Extended Hopf algebras are closely related, but different from, Hopf algebroids. Their definition is motivated by attempting to define cyclic cohomology of Hopf algebroids in general. Many of Hopf algebra like structures, including the Connes-Moscov...

We present a way to turn an arbitrary (unbounded) metric space $\mathcal{M}$ into bounded $\mathcal{B}$ in such that the corresponding Lipschitz-free spaces $\mathcal{F}(\mathcal{M})$ and $\mathcal{F}(\mathcal{B})$ are isomorphic. The construction we provide is functorial weak sense has advantage of being explicit. Apart from its intrinsic theoretical interest, it many applications allows trans...

First we establish a connection between the field of the real numbers and the extended max algebra, based on asymptotic equivalences. Next we propose a further extension of the extended max algebra that will correspond to the field of the complex numbers. Finally we use the analogy between the field of the real numbers and the extended max algebra to define the singular value decomposition of a...

We show that a Lipschitz domain can be expanded solely near a part of its boundary, assuming that the part is enclosed by a piecewise C curve. The expanded domain as well as the extended part are both Lipschitz. We apply this result to prove a regular decomposition of standard vector Sobolev spaces with vanishing traces only on part of the boundary. Another application in the construction of lo...

| Constraint relational databases use constraints to both model and query data. A constraint relation contains a nite set of generalized tuples. Each generalized tuple is represented by a conjunction of constraints on a given logical theory and, depending on the logical theory and the speciic conjunction of constraints, it may possibly represent an in-nite set of relational tuples. For their ch...