Geodesic
$P_\infty$ algebra of KP, free fermions and 2-cocycle in the Lie algebra of pseudodifferential operators
Teoretičeskaâ i matematičeskaâ fizika, Tome 113 (1997) no. 2, pp. 231-260

Voir la notice de l'article provenant de la source Math-Net.Ru

The symmetry algebra $P_\infty=W_\infty\oplus H\oplus I_\infty$ of integrable systems is defined. As an example, the classical Sophus Lie point symmetries of all higher KP equations are obtained. It is shown that one (“positive”) half of the point symmetries belongs to the $W_\infty$ symmetries, while the other (“negative”) part belongs to the $I_\infty$ ones. The corresponding action on the tau-function is obtained for the positive part of the symmetries. The negative part can not be obtained from the free fermion algebra. A new embedding of the Virasoro algebra into $\operatorname{gl}(\infty)$ describes conformal transformations of the KP time variables. A free fermion algebra cocycle is described as a PDO Lie algebra cocycle. 
@article{TMF_1997_113_2_a1,
     author = {P. Winternitz and A. Yu. Orlov},
     title = {$P_\infty$ algebra of {KP,} free fermions and 2-cocycle in the {Lie} algebra of pseudodifferential operators},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {231--260},
     publisher = {mathdoc},
     volume = {113},
     number = {2},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1997_113_2_a1/}
}
TY  - JOUR
AU  - P. Winternitz
AU  - A. Yu. Orlov
TI  - $P_\infty$ algebra of KP, free fermions and 2-cocycle in the Lie algebra of pseudodifferential operators
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1997
SP  - 231
EP  - 260
VL  - 113
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_1997_113_2_a1/
LA  - ru
ID  - TMF_1997_113_2_a1
ER  - 
%0 Journal Article
%A P. Winternitz
%A A. Yu. Orlov
%T $P_\infty$ algebra of KP, free fermions and 2-cocycle in the Lie algebra of pseudodifferential operators
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1997
%P 231-260
%V 113
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_1997_113_2_a1/
%G ru
%F TMF_1997_113_2_a1
P. Winternitz; A. Yu. Orlov. $P_\infty$ algebra of KP, free fermions and 2-cocycle in the Lie algebra of pseudodifferential operators. Teoretičeskaâ i matematičeskaâ fizika, Tome 113 (1997) no. 2, pp. 231-260. http://geodesic.mathdoc.fr/item/TMF_1997_113_2_a1/