**DIPS 1/2003**[tex source, PostScript, PDF file, dvi]-
**Title:**Homogeneous spaces associated with Miura transformations.**Author:**Sergei IGONINFor scalar evolution equations, we prove that a zero-curvature representation with values in a Lie algebra

**g**and a certain type homogeneous space of**g**determine a Miura transformation. Using this result, we show how to construct and classify Miura transformations for a given equation.

Revised version from February 13, 2003, 7 pages, LaTeX-2e (AmSLaTeX).

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