Dirac operator on the quantum fuzzy four-sphere $ S_{qF}^{4} $

Abstract: The q-deformed fuzzy Dirac and chirality operators on quantum fuzzy four-sphere $ S^{4}_{qF} $. Using the q-deformed fuzzy Ginsparg-Wilson algebra, it has been studied the q-deformed fuzzy Dirac and chirality operators in instanton and no-instanton sector. Also, gauged Dirac and chirality operators in both cases have been constructed. It has been showed that In each step our results have correct commutative limit in the limit case when $ q\longrightarrow1 $ and noncommutative parameter $ l $ tends to infinity.