### DIPS 1/98 [tex source, PostScript, PDF file, dvi]

Title: COHOMOLOGY BACKGROUND IN GEOMETRY OF PDE

Author: Joseph KRASIL'SHCHIK

Using techniques of Fr\"olicher\,--\,Nijenhuis brackets, we associate to any formally integrable equation \$\CC{E}\$ a cohomology theory (\$\CC{C}\$-complex) \$H_\CC{C}^*(\CC{E})\$ related to deformations of the equation structure on the infinite prolongation \$\Ei\$. A subgroup in \$H_\CC{C}^1(\CC{E})\$ is identified with recursion operators acting on the Lie algebra \$\sym\CC{E}\$ of symmetries. On the other hand, another subgroup of \$H_\CC{C}^*(\CC{E})\$ can be understood as the algebra of supersymmetries of the ``superization'' of the equation \$\CC{E}\$. This pass to superequations makes it possible to obtain a well-defined action of recursion operators in nonlocal setting. Relations to Poisson structures on \$\Ei\$ are briefly discussed.

18 pages, LaTeX-2e. To compile source files (.tex) one needs the title page style files titlatex.tex.