On the Cohomology of the Lie Algebra Arising from the Lower Central Series of a p-Group
| dc.creator | Mauger, Justin | |
| dc.date | 2003-03-26 | |
| dc.date.accessioned | 2026-07-07T04:56:24Z | |
| dc.date.available | 2026-07-07T04:56:24Z | |
| dc.description | We study the cohomology H*(A) = Ext_A(k,k) of a locally finite, connected, cocommutative Hopf algebra A over k = F_p. Specifically, we are interested in those algebras A for which H*(A) is generated as an algebra by H^1(A) and H^2(A). We shall call such algebras semi-Koszul. Given a central extension of Hopf algebras F --> A --> B with F monogenic and B semi-Koszul, we use the Cartan-Eilenberg spectral sequence and algebraic Steenrod operations to determine conditions for A to be semi-Koszul. Special attention is given to the case in which A is the restricted universal enveloping algebra of the Lie algebra obtained from the mod-p lower central series of a p-group. We show that the algebras arising in this way from extensions by Z/(p) of an abelian p-group are semi-Koszul. Explicit calculations are carried out for algebras arising from rank two p-groups, and it is shown that these are all semi-Koszul for p > 3. | |
| dc.description | 23 pages | |
| dc.identifier | https://arxiv.org/abs/math/0303327 | |
| dc.identifier | http://arxiv.org/abs/math/0303327 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66908 | |
| dc.subject | Rings and Algebras | |
| dc.subject | Algebraic Topology | |
| dc.subject | 16E40 ; 16S30; 16S37 | |
| dc.title | On the Cohomology of the Lie Algebra Arising from the Lower Central Series of a p-Group | |
| dc.type | text |