In this note we analyze the analogy between m-potent and p-central restricted Lie algebras and p-groups. For restricted Lie algebras the notion of m-potency has stronger implications than for p-groups. Every finite-dimensional restricted Lie algebra L is isomorphic to $H/H_{[p]}$ for some finite-dimensional p-central restricted Lie algebra H. In particular, for restricted Lie algebras there does not hold an analogue of J.Buckley's theorem. For p odd one can characterize powerful restricted Lie algebras in terms of the cup product map in the same way as for finite p-groups. Moreover, the p-centrality of the finite-dimensional restricted Lie algebra H has a strong implication on the structure of the cohomology ring $H^\bullet(L,F)$.

On powerful and $p$-central restricted Lie algebras

SICILIANO, Salvatore;
2007

Abstract

In this note we analyze the analogy between m-potent and p-central restricted Lie algebras and p-groups. For restricted Lie algebras the notion of m-potency has stronger implications than for p-groups. Every finite-dimensional restricted Lie algebra L is isomorphic to $H/H_{[p]}$ for some finite-dimensional p-central restricted Lie algebra H. In particular, for restricted Lie algebras there does not hold an analogue of J.Buckley's theorem. For p odd one can characterize powerful restricted Lie algebras in terms of the cup product map in the same way as for finite p-groups. Moreover, the p-centrality of the finite-dimensional restricted Lie algebra H has a strong implication on the structure of the cohomology ring $H^\bullet(L,F)$.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11587/107521
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 3
  • ???jsp.display-item.citation.isi??? 3
social impact