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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Let  be one of the sporadic simple Mathieu groupsM11M_{11},M12M_{12},M22M_{22},M23M_{23}orM24M_{24}, and suppose  is an algebraically closed field of prime characteristic , dividing the order of . In this paper, we describe some of the Lie algebra structure of the first Hochschild cohomology groups of the -blocks ofk⁢GkG. In particular, we calculate the dimension ofHH1⁢(B)\mathrm{HH}^{1}(B)for the -blocks  ofk⁢GkG, and in almost all cases, we determine whetherHH1⁢(B)\mathrm{HH}^{1}(B)is a solvable Lie algebra.

The Lie algebra structure of the degree one Hochschild cohomology of the blocks of the sporadic Mathieu groups