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 modied version o...

To a real Hilbert space and a one-parameter group of orthogonal transformations we associate a C∗-algebra which admits a free quasi-free state. This construction is a freeprobability analog of the construction of quasi-free states on the CAR and CCR algebras. We show that under certain conditions, our C∗-algebras are simple, and the free quasi-free states are unique. The corresponding von Neuma...

One fruitful motivating principle of much research on the family of integrable systems known as “Toda lattices” has been the heuristic assumption that the periodic Toda lattice in an affine Lie algebra is directly analogous to the nonperiodic Toda lattice in a finite-dimensional Lie algebra. This paper shows that the analogy is not perfect. A discrepancy arises because the natural generalizatio...

The paper presents basic concepts of the discrete system theory from the viewpoint of Banach algebras and shows that some Banach algebras of sequences are not only suitable mathematical framework for the multidimensional discrete system theory but also open ways to new models of discrete systems and lead to hitherto unknown methods of homomorphic signal processing and deconvolution. Three Banac...

We compute the Hochschild, cyclic, and periodic cyclic homology groups of algebras of families of Laurent complete symbols on manifolds with corners. We show in particular that the spectral sequence associated with Hochschild homology degenerates at E and converges to Hochschild homology. As a byproduct, we deduce an identification of the space of residue traces on fibrations by manifolds with ...