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

Let $k$ be a field of characteristic $0$, let $\mathsf{C}$ be a finite splitcategory, let $\alpha$ be a 2-cocycle of $\mathsf{C}$ with values in themultiplicative group of $k$, and consider the resulting twisted categoryalgebra $A:=k_\alpha\mathsf{C}$. Several interesting algebras arise that way,for instance, the Brauer algebra. Moreover, the category of biset functors over$k$ is equivalent to a module category over a condensed algebra $\varepsilonA\varepsilon$, for an idempotent $\varepsilon$ of $A$. In [2] the authorsproved that $A$ is quasi-hereditary (with respect to an explicit partial order$\le$ on the set of irreducible modules), and standard modules were givenexplicitly. Here, we improve the partial order $\le$ by introducing a coarserorder $\unlhd$ leading to the same results on $A$, but which allows to pass thequasi-heredity result to the condensed algebra $\varepsilon A\varepsilon$describing biset functors, thereby giving a different proof of a quasi-heredityresult of Webb, see [26]. The new partial order $\unlhd$ has not beenconsidered before, even in the special cases, and we evaluate it explicitly forthe case of biset functors and the Brauer algebra. It also puts furtherrestrictions on the possible composition factors of standard modules.

Quasi-hereditary structure of twisted split category algebras revisited