The aim of this article is to present a detailed algebraic computation of the Hochschild and cyclic homology groups of the Yang–Mills algebras YM(n) (n ∈ ℕ≧2) defined by A. Connes and M. Dubois-Violette in [8], continuing ...

Let G be a group, S = {Si, i ∈ I} a non empty family of (not necessarily distinct) subgroups of infinite index in G and M a ℤ2 G-module. In [4] the authors defined a homological invariant E∗ (G, S, M), which is “dual” to ...

Let G be a group, S = {S-i, i is an element of I} a non empty family of (not necessarily distinct) subgroups of infinite index in G and M a Z(2)G-module. In [4] the authors defined a homological invariant E,(G,S,M), which ...

In this article, I examine the issue of the alleged circularity in the determination of homologies within cladistic analysis. More specifically, I focus on the claims made by the proponents of the dynamic homology approach, ...

Let k be a field, A a unitary associative k-algebra and V a k-vector space endowed with a distinguished element 1V . We obtain a mixed complex, simpler than the canonical one, that gives the Hochschild, cyclic, negative ...

For an extension of associative algebras (Formula presented.) over a field and an (Formula presented.) -bimodule (Formula presented.), we obtain a Jacobi–Zariski long nearly exact sequence relating the Hochschild homologies ...

We study the Hochschild and cyclic homology of noncommutative monogenic extensions. As an application we compute the Hochschild and cyclic homology of the rank 1 Hopf algebras introduced in [L. Krop, D. Radford, Finite ...

Let k be a commutative algebra with Q ⊆ k and let (E,p,i) be a cleft extension of A. We obtain a new mixed complex, simpler than the canonical one, giving the Hochschild and cyclic homologies of E relative to ker(p). This ...

Let f: A → B be a ring homomorphism of not necessarily unital rings and I A an ideal which is mapped by f isomorphically to an ideal of B. The obstruction to excision in K-theory is the failure of the map between relative ...