Periodic cyclic homology of certain nuclear

Relying on properties of the inductive tensor product, we construct cyclic type homology theories for certain nuclear algebras. In this context, we establish continuity theorems. We compute the periodic cyclic homology of the Schwartz algebra of p-adic GL(n) in terms of compactly supported de Rham cohomology of the tempered dual of GL(n). 1. Complete nuclear locally convex algebras Cyclic type homology groups of an algebra A are computed using chain complexes involving tensor powers of A. When A is a general locally convex algebra, this will involve making a choice of a topological tensor product. A locally convex algebra is a locally convex vector space A over C equipped with a separately continuous multiplication. We shall refer to the projective tensor product , the injective tensor product , and the inductive tensor product i .