# On Chevalley-Eilenberg and Cyclic Homologies

@article{Aboughazi1994OnCA, title={On Chevalley-Eilenberg and Cyclic Homologies}, author={R. Aboughazi and Crichton Ogle}, journal={Journal of Algebra}, year={1994}, volume={166}, pages={317-339} }

where H;(_) denotes the Lie algebra homology, HC*(_) cyclic homology, and A is an algebra with unit over a field of characteristic zero. In this paper we give an alternative proof of this theorem which does not involve Weyl's invariant theory for GL(C). We use this approach to compute Chevalley-Eilenberg homology in some interesting new cases. In Section 1, we begin by proving (in characteristic 0) a Leday-QuillenTsygan theorem for complexes which occur as subcomplexes D* of the Chevalley…

## 3 Citations

### 3 0 N ov 2 00 4 Loday – Quillen – Tsygan Theorem for Coalgebras

- Mathematics
- 2008

1 Introduction The original Loday–Quillen–Tsygan Theorem (LQT) is proven by Loday and Quillen [13] and independently by Tsygan [20]. It states that the ordinary Lie homology (here referred as…

### Loday--Quillen--Tsygan Theorem for Coalgebras

- Mathematics
- 2004

In this paper we prove that Loday--Quillen--Tsygan Theorem generalizes to the case of coalgebras. Specifically, we show that the Chevalley--Eilenberg--Lie homology of the Lie coalgebra of infinite…

### Infinitesimal cohomology and the Chern character to negative cyclic homology

- Mathematics
- 2007

There is a Chern character from K-theory to negative cyclic homology. We show that it preserves the decomposition coming from Adams operations, at least in characteristic zero.

## References

SHOWING 1-6 OF 6 REFERENCES

### On the general linear group and Hochschild homology

- Mathematics
- 1985

Our main result here is a rational computation of the homology of the adjoint action of the infinite general linear group of an arbitrary ring. Before stating the result we establish some notation…

### Homologie des algèbres de Leibnitz

- Mathematics
- 1991

L'homologie de hochschild d'une algebre associative unitaire a est la partie primitive d'une nouvelle theorie homologique appliquee a l'algebre de lie des matrices sur a. On introduit une…

### LODAY, Extensions centrales d'algebres de Lie, Ann

- 1950

### BOUSFIELD AND D. KAN, Homotopy limits, completions and localizations

- Springer Lecture Notes
- 1973

### ElLENBERG

- "Homological Algebra," Princeton Univ. Press, Princeton, NJ,
- 1956