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

The equations of open 2-dimensional Toda lattice (TL) correspond toLeznov-Saveliev equations (LSE) interpreted as zero-curvature Yang-Millsequations on the variety of $O(3)$-orbits on the Minkowski space when the gaugealgebra is the image of $\mathfrak{sl}(2)$ under a principal embedding into asimple finite-dimensional Lie algebra $\mathfrak{g}(A)$ with Cartan matrix $A$.The known integrable super versions of TL equations correspond to matrices $A$of two different types. I interpret the super LSE of one type 1 aszero-curvature equations for the \textit{reduced} connection on thenon-integrable distribution on the supervariety of $OSp(1|2)$-orbits on the$N=1$-extended Minkowski superspace; the Leznov-Saveliev method of solution isapplicable only to $\mathfrak{g}(A)$ finite-dimensional and admitting asuperprincipal embedding $\mathfrak{osp}(1|2)\to\mathfrak{g}(A)$. The simplestLSE1 is the super Liouville equation; it can be also interpreted in terms ofthe superstring action. Olshanetsky introduced LSE2 -- another type ofequations of super TL. Olshanetsky's equations, as well as LSE1 withinfinite-dimensional $\mathfrak{g}(A)$, can be solved by the Inverse ScatteringMethod. To interpret these equations remains an open problem, except for thesuper Liouville equation -- the only case where these two types of LSEcoincide. I also review related less known and less popular mathematicalconstructions involved.

Superized Leznov-Saveliev equations as the zero-curvature condition on a reduced connection