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We introduce a Lie algebra, which we call adelic -algebra. Then we construct a natural
bosonic representation and show that the points of the Calogero-Moser spaces are in 1:1
correspondence with the tau-functions in this representation.
The method of contact integrable extensions is used to find new differential coverings for the generalized (2 + 1)-dimensional dispersionless Dym equation and corresponding Bäcklund transformations.
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