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

It is well known that central extensions of a group G correspond to2-cocycles on G. Cocycles can be used to construct extensions of G-gradedalgebras via a version of the Drinfeld twist introduced by Majid. We show how2-cocycles can be defined for an abstract monoidal category C, followingPanaite, Staic and Van Oystaeyen. A braiding on C leads to analogues of Nicholsalgebras in C, and we explain how the recent work on twists of Nichols algebrasby Andruskiewitsch, Fantino, Garcia and Vendramin fits in this context.  Furthermore, we propose an approach to twisting the multiplication in braideddoubles, which are a class of algebras with triangular decomposition over G.Braided doubles are not G-graded, but may be embedded in a double of a Nicholsalgebra, where a twist may be carried out if careful choices are made. This isa source of new algebras with triangular decomposition. As an example, we showhow to twist the rational Cherednik algebra of the symmetric group by thecocycle arising from the Schur covering group, obtaining the spin Cherednikalgebra introduced by Wang.

Cocycle Twists and Extensions of Braided Doubles