It is well known that a generalized q-Schur algebra may be constructed as a quotient of a quantized enveloping algebra U or its modified form U̇. On the other hand, we show here that both U and U̇ may be constructed within an inverse limit of a certain inverse system of generalized q-Schur algebras. Working within the inverse limit Û clarifies the relation between U̇ and U. This inverse limit is a...

We prove that for every singular cardinal μ of cofinality ω, the complete Boolean algebra compPμ(μ) contains a complete subalgebra which is isomorphic to the collapse algebra CompCol(ω1, μ0 ). Consequently, adding a generic filter to the quotient algebra Pμ(μ) = P(μ)/[μ] collapses μ0 to א1. Another corollary is that the Baire number of the space U(μ) of all uniform ultrafilters over μ is equal ...

ABSTRACT In this article we introduce a universal C (∗)-algebras associated to certain simplicial flag complexes. We denote it by [Formula: see text]it is a subalgebra of the noncommutative n-sphere which introduced by J.Cuntz. We present a technical lemma to determine the quotient of the skeleton filtration of a general universal C (∗)-algebra associated to a simplicial flag complex. We examin...

Copyright q 2010 Dongming Cheng. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We introduce a class of noncommutative and noncocommutative weak Hopf algebras with infinite Ext quivers and study their structure. We decompose them...

We associate to each discrete partial dynamical system a universal C-algebra generated by partial isometries satisfying relations given by a Boolean algebra connected to the discrete partial dynamical system in question. We show that for symbolic dynamical systems like one-sided and two-sided shift spaces and topological Markov chains with an arbitrary state space the C-algebras usually associa...

A systematic and exhaustive method based on the group structure of a unitary Lie algebra is proposed to generate an enormous number of quantum codes. With respect to the algebraic structure, the orthogonality condition, which is the central rule of generating quantum codes, is proved to be fully equivalent to the distinguishability of the elements in this structure. In addition, four types of q...

Schematic Kleene algebra with tests (SKAT) supports the equational verification of flowchart scheme equivalence and captures simple while-programs with assignment statements. We formalise SKAT in Isabelle/HOL, using the quotient type package to reason equationally in this algebra. We apply this formalisation to a complex flowchart transformation proof from the literature. We extend SKAT with as...

We identify the ring of odd symmetric functions introduced by Ellis and Khovanov as the space of skew polynomials fixed by a natural action of the Hecke algebra at q = −1. This allows us to define graded modules over the Hecke algebra at q = −1 that are ‘odd’ analogs of the cohomology of type A Springer varieties. The graded module associated to the full flag variety corresponds to the quotient...

In [M. Klin, A. Munemusa, M. Muzychuk, P.-H. Zieschang Directed strongly regular graphs obtained from coherent algebras. Linear Algebra and its Applications 337, (2004) 83-109] the flag algebra of a given balanced incomplete block design with parameters (ν, b, r, k, λ) where λ = 1, has been constructed. In this paper, we consider the association scheme which is related to this flag algebra. By ...

The algebra of basic covers of a graph G, denoted by Ā(G), was introduced by Herzog as a suitable quotient of the vertex cover algebra. In this paper we compute the Krull dimension of Ā(G) in terms of the combinatorics of G. As a consequence, we get new upper bounds on the arithmetical rank of monomial ideals of pure codimension 2. Furthermore, we show that if the graph is bipartite, then Ā(G) ...