2019/11/26 by Carpentier, Sylvain, Suh, Uhi Rinn
#17B69 #17B80 #35Q53 (Primary) 37K10 #37K30 (Secondary) #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.1911.11843
We construct super Hamiltonian integrable systems within the theory of Supersymmetric Poisson vertex algebras (SUSY PVAs). We provide a powerful tool for the understanding of SUSY PVAs called the super master formula. We attach some Lie superalgebraic data to a generalized SUSY W-algebra and show that it is equipped with two compatible SUSY PVA brackets. We reformulate these brackets in terms of odd differential operators and obtain super bi-Hamiltonian hierarchies after performing a supersymmetric analog of the Drinfeld-Sokolov reduction on these operators. As an example, an integrable system is constructed from \mathfrakg=\mathfrakosp(2|2).