Fibonacci代数的Hochschild同调群

设Λd是Fibonacci代数,基于对Bardzell极小投射双模分解的细致分析,用组合的方法清晰地计算了Fibonacci代数Λd的各阶Hochschild同调群的维数.     

Leibniz and Hochschild homology

We construct and study the map from Leibniz homology HL_?(𝔥) of an abelian extension 𝔥 of a simple real Lie algebra 𝔤 to the Hochschild homology HH_??1(U(𝔥)) of the universal envelopping algebra U(𝔥). To calculate some homology groups, we use the Hochschild-Serre spectral sequences and Pirashvili spectral sequences. The result shows what part of the non-commutative Leibniz theory is detected by classical Hochschild homology, which is of interest today in string theory.     

Hochschild homology and split pairs

We study the Hochschild homology of algebras related via split pairs, and apply this to fiber products, trivial extensions, monomial algebras, graded-commutative algebras and quantum complete intersections. In particular, we compute lower bounds for the dimensions of both the Hochschild homology and cohomology groups of quantum complete intersections.     

Topological Hochschild homology of number rings

We calculate an explicit formula for the topological Hochschild homology of a discrete valuation ring of characteristic zero with finite residue field. From this we deduce the topological Hochschild homology of global number rings.

     

On the homology spectral sequence for topological Hochschild homology

Marcel Bökstedt has computed the homotopy type of the topological Hochschild homology of using his definition of topological Hochschild homology for a functor with smash product. Here we show that easy conceptual proofs of his main technical result of are possible in the context of the homotopy theory of -algebras as introduced by Elmendorf, Kriz, Mandell and May. We give algebraic arguments based on naturality properties of the topological Hochschild homology spectral sequence. In the process we demonstrate the utility of the unstable ``lower' notation for the Dyer-Lashof algebra.

     

Finite generation of Hochschild homology algebras

We prove converses of the Hochschild-Kostant-Rosenberg Theorem, in particular: If a commutative algebra S is flat and essentially of finite type over a noetherian ring , and the Hochschild homology HH _* (S|) is a finitely generated S-algebra for shuffle products, then S is smooth over . Oblatum 27-V-1999 & 27-IX-1999 / Published online: 24 January 2000     

The module structure of Hochschild homology in some examples

In this Note we give a simple proof of a conjecture by A. Căldăraru stating the compatibility between the modified Hochschild–Kostant–Rosenberg isomorphism and the action of Hochschild cohomology on Hochschild homology in the case of Calabi–Yau manifolds and smooth projective curves. To cite this article: E. Macri` et al., C. R. Acad. Sci. Paris, Ser. I 346 (2008).     

Hochschild homology of rings of algebraic integers

The purpose of this paper is to remind that the André-Quillen homology theory is a very useful tool to study Hochschild homology of commutative algebras. We choose as an example a computation of Hochschild homology of Dedekind extensions.     

Hochschild homology criteria for trivial algebra structures

We prove two similar results by quite different methods. The first one deals with augmented artinian algebras over a field: we characterize the trivial algebra structure on the augmentation ideal in terms of the maximality of the dimensions of the Hochschild homology (or cyclic homology) groups. For the second result, let be a 1-connected finite CW-complex. We characterize the trivial algebra structure on the cohomology algebra of with coefficients in a fixed field in terms of the maximality of the Betti numbers of the free loop space.

     

Cyclic and Hochschild homology of 2-nilpotent algebras

We compute the cyclic homology of a 2-nilpotent algebra, using a reduced way of obtaining it for an algebra containing a separable subalgebra as a direct summand.Supported by the Swiss National Foundation, FNSRS.     

Hochschild (Co)homology of Exterior Algebras

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 generators and relations.     

Hochschild and cyclic homology of finite type algebras

We study Hochschild and cyclic homology of finite type algebras using abelian stratifications of their primitive ideal spectrum. Hochschild homology turns out to have a quite complicated behavior, but cyclic homology can be related directly to the singular cohomology of the strata. We also briefly discuss some connections with the representation theory of reductive p-adic groups.     

On galois descent for Hochschild and cyclic homology

LetG be a finite group acting by automorphisms on an algebraS over some commutative ringk. We show that if the action ofG restricted to the center ofS is Galois in the sense of [C-H-R], thenHH _*(S ^G)≊HH _* (S) ^G. An analogous result holds for cyclic homology, provided the order ofG is invertible ink. The author was supported in part by a grant from the NSF.