Back to Search
Start Over
On homology of Lie algebras over commutative rings
- Source :
- Journal of Algebra, Volume 586, 2021, Pages 99-139, ISSN 0021-8693
- Publication Year :
- 2020
-
Abstract
- We study five different types of the homology of a Lie algebra over a commutative ring which are naturally isomorphic over fields. We show that they are not isomorphic over commutative rings, even over $\mathbb Z,$ and study connections between them. In particular, we show that they are naturally isomorphic in the case of a Lie algebra which is flat as a module. As an auxiliary result we prove that the Koszul complex of a module $M$ over a principal ideal domain that connects the exterior and the symmetric powers $0\to \Lambda^n M\to M \otimes \Lambda^{n-1} M \to \dots \to S^{n-1}M \otimes M \to S^nM\to 0 $ is purely acyclic.
- Subjects :
- Mathematics - K-Theory and Homology
Subjects
Details
- Database :
- arXiv
- Journal :
- Journal of Algebra, Volume 586, 2021, Pages 99-139, ISSN 0021-8693
- Publication Type :
- Report
- Accession number :
- edsarx.2010.00369
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1016/j.jalgebra.2021.06.019