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

We review the list of non-degenerate invariant (super)symmetric bilinearforms (briefly: NIS) on the following simple (relatives of) Lie(super)algebras: (a) with symmetrizable Cartan matrix of any growth, (b) withnon-symmetrizable Cartan matrix of polynomial growth, (c) Lie (super)algebrasof vector fields with polynomial coefficients, (d) stringy a.k.a.superconformal superalgebras, (e) queerifications of simple restricted Liealgebras.  Over algebraically closed fields of positive characteristic, we establishwhen the deform (i.e., the result of deformation) of the knownfinite-dimensional simple Lie (super)algebra has a NIS. Amazingly, in most ofthe cases considered, if the Lie (super)algebra has a NIS, its deform has a NISwith the same Gram matrix after an identification of bases of the initial anddeformed algebras. We do not consider odd parameters of deformations.  Closely related with simple Lie (super)algebras with NIS is the notion ofdoubly extended Lie (super)algebras of which affine Kac--Moody (super)algebrasare the most known examples.

Non-degenerate invariant (super)symmetric bilinear forms on simple Lie (super)algebras