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

We investigate several categories of integrable $sl(\infty)$-, $o(\infty)$-,$sp(\infty)$-modules. In particular, we prove that the category of integrable$sl(\infty)$-, $o(\infty)$-, $sp(\infty)$-modules with finite-dimensionalweight spaces is semisimple. The most interesting category we study is thecategory $\widetilde{\mathrm{Tens}}_{\mathfrak{g}}$ of tensor modules. Itsobjects $M$ are defined as integrable modules of finite Loewy length such thatthe algebraic dual $M^*$ is also integrable and of finite Loewy length.  We prove that the simple objects of$\widetilde{\mathrm{Tens}}_{\mathfrak{g}}$ are precisely the simple tensormodules, i.e. the simple subquotients of the tensor algebra of the direct sumof the natural and conatural representations.  We also study injectives in $\widetilde{\mathrm{Tens}}_{\mathfrak{g}}$ andcompute the Ext$^1$'s between simple modules. Finally, we characterize acertain subcategory $\mathrm{Tens}_{\mathfrak{g}}$ of$\widetilde{\mathrm{Tens}}_{\mathfrak{g}}$ as the unique minimal abelian fullsubcategory of the category of integrable modules which contains a non-trivialmodule and is closed under tensor product and algebraic dualization.

Categories of integrable $sl(\infty)$-, $o(\infty)$-, $sp(\infty)$-modules