**DIPS 15/2001**[tex source, PostScript, PDF file, dvi]-
**Title:**ON ONE-PARAMETRIC FAMILY OF B\"ACKLUND AUTOTRANSFORMATIONS FOR THE LIOUVILLE EQUATION.

**Author:**Arthemy V. KiselevScaling symmetry of the Liouville equation is proved to provide a one-parametric family of one-dimensional non-abelian coverings determining a B\"acklund autotransformation. Deformation of the structural element is shown to be equal to the Fr\"olicher-Nijenhuis bracket of the symmetry lifting and the structural element of the coverings. An intriguing by-formula in total derivatives is obtained.

7 pages, LaTeX-2e (AmS-LaTeX).

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