Noncommutative Application of a Homotopy Deformed Differential Graded Algebra with its Hodge Theory

DOI: 10.5176/2251-1911_CMCGS16.31

Authors: G. Y. Alhamzi and E. J. Beggs

Abstract: The deformation of a differential graded algebra (DGA) can be applied to noncommutative calculus. As a specific example of the deformation, we use the standard Podle\'s non commutative sphere $S^2_q$ and its differential calculus. We then study the resulting operator $ \Delta $ on the noncommutative sphere, and its Hodge theory giving the eigenvalues and eigenfunctions on $ \Omega S^{2}_{q}$.

Keywords: It\^o Calculus, Hodge Theory, Noncommutative Sphere