A noncommutative Sierpinski Gasket

A quantized version of the Sierpinski gasket is proposed, on purely topological grounds. This is a C∗-algebra with a suitable form of self-similarity. Properties of this C∗algebra are studied, in particular irreducible representations and extremal traces are fully described. A self-similar Dirichlet form together with a spectral triple are also constructed, extending results already known for the classical gasket.

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