‎from hilbert's theorem of zeroes‎, ‎and from noether's ideal theory‎, ‎birkhoff derived certain algebraic concepts (as explained by tholen) that have a dual significance in general toposes‎, ‎similar to their role in the original examples of algebraic geometry‎. ‎i will describe a simple example that illustrates some of the aspects of this relationship‎. the dualization from algebra ...

Let A be a partial *-algebra endowed with a topology τ that makes it into a locally convex topological vector space A[τ ]. Then A is called a topological partial *-algebra if it satisfies a number of conditions, which all amount to require that the topology τ fits with the multiplier structure of A. Besides the obvious cases of topological quasi *-algebras and CQ*-algebras, we examine several c...

We present a class of subshifts ZN , N = 1, 2, . . . whose associated C∗-algebras OZN are simple, purely infinite and not stably isomorphic to any Cuntz-Krieger algebra nor to Cuntz algebra. The class of the subshifts is the first examples whose associated C∗-algebras are not stably isomorphic to any Cuntz-Krieger algebra nor to Cuntz algebra. The subshifts ZN are coded systems whose languages ...

Let H be a bialgebra. An H-module-algebra is an associative algebra A that is also an H-module such that the multiplication map on A becomes an H-module morphism. This algebraic structure arises often in algebraic topology, quantum groups [11, Chapter V.6], Lie and Hopf algebras theory [3, 16, 19], and group representations [1, Chapter 3]. For example, in algebraic topology, the complex cobordi...

We analyze topological string theory on a two dimensional torus, focusing on symmetries in the matter sector. Even before coupling to gravity, the topological torus has an infinite number of point-like physical observables, which give rise via the BRST descent equations to an infinite symmetry algebra of the model. The point-like observables of ghost number zero form a topological ground ring, ...

Let Ω be a circular domain, that is, an open disk with finitely many closed disjoint disks removed. Denote by H(Ω) the Banach algebra of all bounded holomorphic functions on Ω, with pointwise operations and the supremum norm. We show that the topological stable rank of H(Ω) is equal to 2. The proof is based on Suarez’s theorem that the topological stable rank of H(D) is equal to 2, where D is t...