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

Derived equivalences between finite dimensional algebras do, in general, notpass to centraliser (or other) subalgebras, nor do they preserve homologicalinvariants of the algebras, such as global or dominant dimension. We show that,however, they do so for large classes of algebras described in this article.  Algebras $A$ of $\nu$-dominant dimension at least one have unique largestnon-trivial self-injective centraliser subalgebras $H_A$. A derived restrictiontheorem is proved: A derived equivalence between $A$ and $B$ implies a derivedequivalence between $H_A$ and $H_B$.  Two methods are developed to show that global and dominant dimension arepreserved by derived equivalences between algebras of $\nu$-dominant dimensionat least one with anti-automorphisms preserving simples, and also betweenalmost self-injective algebras. One method is based on identifying particularderived equivalences preserving homological dimensions, while the other methodidentifies homological dimensions inside certain derived categories.  In particular, derived equivalent cellular algebras have the same globaldimension. As an application, the global and dominant dimensions of blocks ofquantised Schur algebras with $n \geq r$ are completely determined.

Derived equivalences, restriction to self-injective subalgebras and invariance of homological dimensions