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 $A=A(\alpha, \beta)$ be a graded down-up algebra with $({\rm deg}\,x,{\rm deg}\,y)=(1,n)$ and $\beta \neq 0$, and let $\nabla A$ be the Beilinsonalgebra of $A$. If $n=1$, then a description of the Hochschild cohomology groupof $\nabla A$ is known. In this paper, we calculate the Hochschild cohomologygroup of $\nabla A$ for the case $n \geq 2$. As an application, we see that thestructure of the bounded derived category of the noncommutative projectivescheme of $A$ is different depending on whether $\left(\begin{smallmatrix} 1&0\end{smallmatrix}\right)\left(\begin{smallmatrix} \alpha &1 \\ \beta &0\end{smallmatrix}\right)^n\left(\begin{smallmatrix} 1 \\ 0\end{smallmatrix}\right)$ is zero or not. Moreover, it turns out that there isa difference between the cases $n=2$ and $n\geq 3$ in the context ofGrothendieck groups.

Hochschild cohomology related to graded down-up algebras with weights $(1,n)$