The central result here is an explicit computation of the Hochschild and cyclic homologies of a natural smooth subalgebra of stable continuous trace algebras having smooth manifolds X as their spectrum. More precisely, the Hochschild homology is identified with the space of differential forms on X, and the periodic cyclic homology with the twisted de Rham cohomology of X, thereby generalizing s...

A generalization of the cyclic Jacobi algorithm is proposed that works in an arbitrary compact Lie algebra. This allows, in particular, a unified treatment of Jacobi algorithms on different classes of matrices, such as, e.g., skew-symmetric or skew-Hermitian Hamiltonian matrices. Wildberger has established global, linear convergence of the algorithm for the classical Jacobi method on compact Li...

The genesis of this paper is the construction of a new operator that, when combined with a theorem of Herrero, settles a question of Herrero. Herrero proved that a strictly cyclic operator on an infinite dimensional Hilbert space is never triangular. He later asks whether the adjoint of a strictly cyclic operator is necessarily triangular. We settle the question by constructing an operator T fo...

We propose a construction of lattices from (skew-) polynomial codes, by endowing quotients some ideals in both number fields and cyclic algebras with suitable trace form. give criteria for unimodularity. This yields integral unimodular multiplicative structure. Examples are provided.

The stabilization of Hochschild homology of commutative algebras is Gamma homology. We describe a cyclic variant of Gamma homology and prove that the associated analogue of Connes’ periodicity sequence becomes almost trivial, because the cyclic version coincides with the ordinary version from homological degree two on. We offer an alternative explanation for this by proving that the B-operator ...

In this paper we prove that the noncyclic generic abelian crossed product p-algebras constructed by Amitsur and Saltman in [AS78] remain noncyclic after tensoring by any prime to p extension of their centers. We also prove that an example due to Saltman of an indecomposable generic abelian crossed product with exponent p and degree p 2 remains indecomposable after any prime to p extension. 0 In...

Let A be a unital separable simple C∗-algebra with TR(A) ≤ 1 and α be an automorphism. We show that if α satisfies the tracially cyclic Rokhlin property then TR(A ⋊α Z) ≤ 1. We also show that whenever A has a unique tracial state and αm is uniformly outer for each m and αr is approximately inner for some r > 0, α satisfies the tracial cyclic Rokhlin property. By applying the classification theo...