Non Commutative Geometry On U(sb(2))

Noncommutative geometry on the universal envelopping algebra of the Borel subgroup U(sb(2, C)) ARM Boris arm.boris@gmail.com Abstract We study the Borel algebra define by [xa, xb] = 2λδa,1xb as a noncommutative manifold R3 λ. We calculate its noncommutative... More

Noncommutative geometry on the universal envelopping algebra of the Borel subgroup U(sb(2, C)) ARM Boris arm.boris@gmail.com Abstract We study the Borel algebra define by [xa, xb] = 2λδa,1xb as a noncommutative manifold R3 λ. We calculate its noncommutative differential form relations. We deduce its partial derivative relations and the derivative of a plane wave. After calculating its de Rham cohomology, we deduce the wave operator and its corresponding magnetic solution. Less