since 2005 a new powerful invariant of an algebra has emerged using the earlier work of horvath, hethelyi, kulshammer and murray. the authors studied morita invariance of a sequence of ideals of the center of a nite dimensional algebra over a eld of nite characteristic. it was shown that the sequence of ideals is actually a derived invariant, and most recently a slightly modied version o...

We compute periodic, analytic and local cyclic cohomology for convolution algebras of compact Lie groups in order to exhibit differences between these theories. A surprising result is that the periodic and analytic cyclic cohomology of the smooth convolution algebras differ, although these algebras have finite homological dimension.

We generalise the known excision results for Hochschild, cyclic and periodic cyclic homology to algebras in symmetric monoidal categories. Our abstract result also contains excision for extensions of nuclear H-unital Fréchet algebras. As an application, we compute the Hochschild and cyclic homology of the algebra of Whitney functions on an arbitrary closed subset of a smooth manifold, and the p...

Abstract. In this paper, we provide a new formulation for the generalized periodic Toda lattice. Since the work of Kostant, Adler and Symes, it has been known that the Toda lattice is related to the structure of simple Lie algebras. Indeed, the non-periodic and the periodic Toda lattices can be expressed as Hamiltonian systems on coadjoint orbits: the former of a simple Lie group and the latter...

Given an object in a category, we study its orbit algebra with respect to an endofunctor. We show that if the object is periodic, then its orbit algebra modulo nilpotence is a polynomial ring in one variable. This specializes to a result on Ext-algebras of periodic modules over Gorenstein algebras. We also obtain a criterion for an algebra to be of wild representation

Abstract. In this paper, we introduce a Z-graded variant of the periodic cyclic homology of associative algebras which generalizes the infinitesimal cohomology of affine algebras in characteristic 0 and show that it satisfies the K0nneth formula (i.e. it commutes with the formation of tensor products). We also show that the Kllnneth formula in periodic cyclic homology holds only under the prese...