The cohomology of Lie (super)algebras has many important applications in mathematics and physics. It carries most fundamental (“topological”) information about algebra under consideration. At present, because of the need for very tedious algebraic computation, the explicitly computed cohomology for different classes of Lie (super)algebras is known only in a few cases. That is why application of...

Abstract. A graphical expansion formula for non-commutative matrix integrals with values in a finite-dimensional real or complex von Neumann algebra is obtained in terms of ribbon graphs and their non-orientable counterpart called Möbius graphs. The contribution of each graph is an invariant of the topological type of the surface on which the graph is drawn. As an example, we calculate the inte...

Starting from a N = 1 scalar supermultiplet in 2+1 dimensions, we demonstrate explicitly the appearance of induced N = 1 vector and scalar supermultiplets of composite operators made out of the fundamental supersymmetric constituents. We discuss an extension to a N = 2 super-algebra with central extension, due to the existence of topological currents in 2+1 dimensions. As a specific model we co...

In this article a general framework for studying analytic representations of a real Lie group G is introduced. Fundamental topological properties of the representations are analyzed. A notion of temperedness for analytic representations is introduced, which indicates the existence of an action of a certain natural algebra A(G) of analytic functions of rapid decay. For reductive groups every Har...

We consider the transformation ev which associates to any element in a K-algebra A a function on the the set of its K-points. This is the analogue of the fundamental Gelfand transform. Both ev and its dual ev * are the maps from a discrete K-module to a topological K-module and we investigate in which case the image of each map is dense. The answer is nontrivial for various choices of K and A a...

For a locally path connected topological space, the topological fundamental group is discrete if and only if the space is semilocally simplyconnected. While functoriality of the topological fundamental group for arbitrary topological spaces remains an open question, the topological fundamental group is always a homogeneous space.

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...