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 Tools annual

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 monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Rota-Baxter operators and more generally $\mathcal{O}$-operators onassociative algebras are important in probability, combinatorics, associativeYang-Baxter equation and splitting of algebras. Using a method of Uchino, weconstruct an explicit graded Lie algebra whose Maurer-Cartan elements are givenby $\mathcal{O}$-operators. This allows us to construct a cohomology for an$\mathcal{O}$-operator. This cohomology can also be seen as the Hochschildcohomology of a certain algebra with coefficients in a suitable representation.Next, we study linear and formal deformations of an $\mathcal{O}$-operatorwhich are governed by the above-defined cohomology. We introduce Nijenhuiselements associated with an $\mathcal{O}$-operator which give rise to trivialdeformations. As an application, we conclude deformations of weight zeroRota-Baxter operators and associative {\bf r}-matrices.

Deformations of associative Rota-Baxter operators