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We study the Borel algebra de ne by [x a ; x b ] = 2 a;1 x b as anoncommutative manifold R 3 . We calculate its noncommutative di erential formrelations. We deduce its partial derivative relations and the derivative of aplane wave. After calculating its de Rham cohomology, we deduce the waveoperator and its corresponding magnetic solution.

Noncommutative geometry on the universal envelopping algebra of the Borel subgroup U[sb(2)]