Appears in collection : Workshop on Differential Geometry and Nonassociative Algebras / Colloque en géométrie différentielle et algèbres non associatives

We show that the spectrum of fundamental particles of matter and their symmetries can be encoded in a finite quantum geometry equipped with a supplementary structure connected with the quark-lepton symmetry. The occurrence of the exceptional quantum geometry for the description of the standard model with 3 generations is suggested. We discuss the field theoretical aspect of this approach taking into account the theory of connections on the corresponding Jordan modules.