A simple sufficient condition for certain cyclic algebras of odd degree d to be split is presented. It employs certain binary forms of degree d and the values they represent. A similar sufficient condition for certain Albert algebras not to be division algebras is found as well.

Hopf algebras, cyclic cohomology and the transverse index theorem

We present families of unital algebras obtained through a doubling process from a cyclic central simple algebra D = (K/F, σ, c), employing a K-automorphism τ and an element d ∈ D×. These algebras appear in the construction of iterated spacetime block codes. We give conditions when these iterated algebras are division which can be used to construct fully diverse iterated codes. We also briefly l...

The minimal projective bimodule resolutions of the exterior algebras are explicitly constructed. They are applied to calculate the Hochschild (co)homology of the exterior algebras. Thus the cyclic homology of the exterior algebras can be calculated in case the underlying field is of characteristic zero. Moreover, the Hochschild cohomology rings of the exterior algebras are determined by generat...

We present families of unital algebras obtained through a doubling process from a cyclic central simple algebra D = (K/F, σ, c), employing a K-automorphism τ and an element d ∈ D. These algebras appear in the construction of iterated spacetime block codes. We give conditions when these iterated algebras are division which can be used to construct fully diverse iterated codes. We also briefly lo...

We determine the periodic cyclic homology of the Iwahori-Hecke algebras Hq, for q ∈ C∗ not a “proper root of unity.” (In this paper, by a proper root of unity we shall mean a root of unity other than 1.) Our method is based on a general result on periodic cyclic homology, which states that a “weakly spectrum preserving” morphism of finite type algebras induces an isomorphism in periodic cyclic ...

The minimal projective bimodule resolutions of the exterior algebras are explicitly constructed. They are applied to calculate the Hochschild (co)homology of the exterior algebras. Thus the cyclic homology of the exterior algebras can be calculated in case the underlying field is of characteristic zero. Moreover, the Hochschild cohomology rings of the exterior algebras are determined by generat...

Introduction. In this paper we present a detailed account of the results recently published in the Proceedings of the National Academy of Sciences [29 Our theory is an attempt to generalize the results of the classical class field theory to arbitrary normal fields. In the last analysis, the theory of cyclic extensions Z of an algebraic number field k can be described in terms of cyclic algebras...

In this work we consider the moduli space of all noncommutative metric Lie algebras, having a nondegenerate symmetric invariant bilinear form, over $\mathbb C$ and R$ up to dimension 5 algebras in 6. We introduce cyclic reduced cohomology identify their deformations.