This article is cited in 1 paper

Bosonic symmetries of the extended fermionic $(2N,2M)$-Toda hierarchy

Chuanzhong Li

Department of Mathematics, Ningbo University, Ningbo, Zhejiang, China

Abstract: We construct the additional symmetries of the fermionic $(2N,2M)$-Toda hierarchy based on a generalization of the $N=(1|1)$ supersymmetric two-dimensional Toda lattice hierarchy. These additional flows constitute a $w_\infty\times w_\infty$ Lie algebra. As a bosonic reduction of the $N=(1|1)$ supersymmetric two-dimensional Toda lattice hierarchy and the fermionic $(2N,2M)$-Toda hierarchy, we define a new extended fermionic $(2N,2M)$-Toda hierarchy that admits a bosonic Block-type superconformal structure.

Keywords: $N=(1|1)$ supersymmetric Toda hierarchy, extended fermionic $(2N,2M)$-Toda hierarchy, additional symmetry, Block algebra.

PACS: 02.20.Sv, 02.30.Ik, 11.30.Pb.

Received: 20.07.2018
Revised: 20.07.2018

DOI: 10.4213/tmf9605

 English version: Theoretical and Mathematical Physics, 2019, 199:2, 695–708

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