English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We show, for a field ${\mathbb F}$ of prime characteristic $p>0$, that thetruncated filiform Lie algebra ${\frak m}_0(p)$ admits a family ${\frakm}_0^\lambda(p)$ of restricted Lie algebra structures parameterized by elements$\lambda\in {\mathbb F}^p$. We compute the ordinary cohomology groups$H^q({\frak m}_0^\lambda(p))$ and restricted cohomology groups $H^q_*({\frakm}_0^\lambda(p))$ for $q=1, 2$, and we give explicit descriptions of bases forthese cohomology spaces. We apply our results to restricted one-dimensionalcentral Extensions of the algebras ${\frak m}_0^\lambda(p)$.

Restricted One-dimensional Central Extensions of the Restricted Filiform Lie Algebras ${\frak m}_0^\lambda(p)$