Ben-Gurion University, Jacob Blaustein Institute for Desert Research,
Sede-Boker Campus, 84990, ISRAEL;
Department of Applied Research,
Institute of Mathematics of NAS of Ukraine,
3 Tereshchenkivs'ka Str.,
01601 Kyiv-4, UKRAINE

(Non)Locality of symmetries and Poisson structures generated using hereditary recursion operators and proof of the Novikov-Maltsev conjecture

For a large class of  hereditary recursion operators (ROs), including overwhelming majority of ROs of (1+1)-dimensional integrable systems known today, we present new easily verifiable sufficient conditions of locality of symmetries generated by these ROs. Note that unlike the earlier work of Sanders and Wang, we do not assume homogeneity and time-independence of coefficients of ROs in question. Using the above result we prove, under fairly mild assumptions, the recent conjecture of S.P. Novikov and A.Ya. Maltsev on the structure of nonlocal terms of higher Poisson structures generated by the hereditary ROs.