We construct a simplicial locally convex algebra, whose weak dual is the standard cosimplicial topological space. The construction is carried out in a purely categorical way, so that it can be used to construct (co)simplicial objects in a variety of categories — in particular, the standard cosimplicial topological space can be produced.

The multiplicative group of a global field acts on its adele ring by multiplication. We consider the crossed product algebra of the resulting action on the space of Schwartz functions on the adele ring and compute its Hochschild, cyclic and periodic cyclic homology. We also compute the topological K-theory of the C-algebra crossed product.

We study the “Lie Algebra” of the group of Gauge Transformations of Space-time. We obtain topological invariants arising from this Lie Algebra. Our methods give us fresh mathematical points of view on Lorentz Transformations, orientation conventions, the Doppler shift, Pauli matrices, Electro-Magnetic Duality Rotation, Poynting vectors, and the Energy Momentum Tensor T .

In this talk we give a brief review of the algebraic structure behind the open and closed topological strings and D-branes and emphasize the role of tensor category and the Frobenius algebra. Also, we speculate on the possibility of generalizing the topological strings and the D-branes through the subfactor theory.

Let I be any index set. We consider the Banach algebra Ce + l(I) with the Hadamard product, and prove that its Bass and topological stable ranks are both equal to 1. We also characterize divisors, maximal ideals, closed ideals and closed principal ideals. For I = N we also characterize all prime z-ideals in this Banach algebra.

We study the ”Lie Algebra” of the group of Gauge Transformations of Space-time. We obtain topological invariants arising from this Lie Algebra. Our methods give us fresh mathematical points of view on Lorentz Transformations, orientation conventions, the Doppler shift, Pauli matrices , Electro-Magnetic Duality Rotation, Poynting vectors, and the Energy Momentum Tensor T .

In this article we analyze a two dimensional lattice gauge theory based on a quantum group. The algebra generated by gauge fields is the lattice algebra introduced recently by A. in [1]. We define and study Wilson loops. This theory is quasi-topological as in the classical case, which allows us to compute the correlation functions of this theory on an arbitrary surface.

We study the ”Lie Algebra” of the group of Gauge Transformations of Space-time. We obtain topological invariants arising from this Lie Algebra. Our methods give us fresh mathematical points of view on Lorentz Transformations, orientation conventions, the Doppler shift, Pauli matrices , Electro-Magnetic Duality Rotation, Poynting vectors, and the Energy Momentum Tensor T .

Papert Strauss (Proc. London Math. Soc. 18(3), 217–230, 1968) used Pontryagin duality to prove that a compact Hausdorff topological Boolean algebra is a powerset algebra. We give a more elementary proof of this result that relies on a version of Bogolyubov’s lemma.

An action of Zk is associated to a higher rank graph Λ satisfying a mild assumption. This generalises the construction of a topological Markov shift arising from a nonnegative integer matrix. We show that the stable Ruelle algebra of Λ is strongly Morita equivalent to C∗(Λ). Hence, if Λ satisfies the aperiodicity condition, the stable Ruelle algebra is simple, stable and purely infinite.