A Banach algebra A with radical R is said to have property (S) if the natural mapping from the algebraic tensor product 2 A ® A onto A is open, when A ® A is given the protective norm. The purpose of this note is to provide a counterexample to Zinde's claim that when A is commutative and R is one dimensional the fulfillment of property (S) in A implies its fulfillment in the quotient algebra A/R .

1 Under the microscope 1.1 Osculating spaces of homogeneous varieties Let G be a simply connected complex semisimple Lie group, g its Lie algebra, and g its tensor algebra. The universal envelopping algebra of U(g) is the quotient of this tensor algebra by the ideal generated by the elements xy ? yx ? x; y], x; y 2 g. This quotient algebra inherits a ltration from the natural grading of the ten...

We employ the notions of ‘sequential function’ and ‘interrogation’ (dialogue) in order to define new partial combinatory algebra structures on sets of functions. These structures are analyzed using J. Longley’s preorder-enriched category of partial combinatory algebras and decidable applicative structures. We also investigate total combinatory algebras of partial functions. One of the results i...

In this paper, we first show that the irreducible characters of a quotient table algebra modulo a normal closed subset can be viewed as the irreducible characters of the table algebra itself. Furthermore, we define the character products for table algebras and give a condition in which the products of two characters are characters. Thereafter, as a main result we state and prove the Burnside-Br...

Introduction Let B = k[x 1 ,. .. , x n ] be a polynomial ring over a field k and A = B/J a quotient ring of B by a homogeneous ideal J. Let m denote the maximal graded ideal of A. Then the Rees algebra R = A[mt] may be considered a standard graded k-algebra and has a presentation B[y 1 ,. In this paper we want to compare the ideals J and I J as well as their homological properties.

Let F be a local non-Archimedean field with ring of integers o and uniformizer ̟. Let X be a one-dimensional formal o-module of F -height n over the algebraic closure F of the residue field of o. By the work of Drinfeld, the universal deformation X of X is a formal group over a power series ring R0 in n − 1 variables over the completion of the maximal unramified extension ônr of o. For h ∈ {0, ....

We study quotients of quasi-affine schemes by unipotent groups over fields of characteristic 0. To do this, we introduce a notion of stability which allows us to characterize exactly when a principal bundle quotient exists and, together with a cohomological vanishing criterion, to characterize whether or not the resulting quasi-affine quotient scheme is affine. We completely analyze the case of...

Zhedanov’s algebra AW (3) is considered with explicit structure constants such that, in the basic representation, the first generator becomes the second order q-difference operator for the Askey–Wilson polynomials. It is proved that this representation is faithful for a certain quotient of AW (3) such that the Casimir operator is equal to a special constant. Some explicit aspects of the double ...

A central principle of this paper is that, for a finitely presented group G, the algebraic properties of its finite index subgroups should be reflected by the geometry of its finite quotients. These quotients can indeed be viewed as geometric objects, in the following way. If we pick a finite set of generators for G, these map to a generating set for any finite quotient and hence endow this quo...

Let X be a smooth projective curve over C which admits a finite group G of automorphisms. Then G×G acts on the product surface Y = X ×X, and so for each subgroup H ≤ G×G, the quotient Z = H\Y is a normal algebraic surface. Here we shall restrict attention to the case that the subgroup H is the graph of a group automorphism α ∈ Aut(G) of G, i.e. H = ∆α = {(g, α(g)) : g ∈ G}; we propose to call t...