International Conference on Algebra, Topology and Topological Algebras

The First ICATTA will be held at the city of Veracruz in the eastern state of Veracruz in Mexico, during the first week of the year 2011 (January 5^th to 7^th).

The essential character of topological algebras is the simultaneous consideration of two structures on the same set. An algebraic structure (that of an algebra) and a topological structure, ensuring the consistency in between algebra and topology, leading as vital components, to an important object of Functional Analysis that we call topological algebras.

The study of (non-normed) topological algebras began around 1950, to manipulate certain classes of non-normed topological algebras that appeared naturally in mathematics and physics. Some results on such topological algebras had already published earlier in 1947 by R. Arens. It was only in 1952 when Arens and E.A. Michael gave, independently, the first systematic study on locally m-convex algebras that constitute an important class of non-normed topological algebras. Here, one can stress the fact that M. A. Naimark, an expert in the area of Banach algebras, had remarked (in 1950) the importance of consideration of non-normed algebras and predicted the development of their theory. Concerning cosmology, G. Lassner, to his great surprise, realized that the theory of normed topological algebras was not enough to work with.

In addition to the study of the internal structure of non-normed and even non-locally convex topological algebras, there are applications to other branches of mathematics, such as differential geometry of smooth manifolds, and mathematical physics, for instance, quantum relativity (A. Mallios) and quantum cosmology (G. Lassner). Further, topological algebras aim to rule over unbounded operators. Other topics where topological algebras are applicable are topological homological algebra, topological algebraic geometry, sheaf theory and K-theory.

More information in event's page: ICATTA 2011