TY - JOUR T1 - Quantum gauge symmetries in noncommutative geometry Y1 - 2014 A1 - Jyotishman Bhowmick A1 - Francesco D'Andrea A1 - Biswarup Krishna Das A1 - Ludwik Dabrowski AB - We discuss generalizations of the notion of i) the group of unitary elements of a (real or complex) finite-dimensional C*-algebra, ii) gauge transformations and iii) (real) automorphisms in the framework of compact quantum group theory and spectral triples. The quantum analogue of these groups are defined as universal (initial) objects in some natural categories. After proving the existence of the universal objects, we discuss several examples that are of interest to physics, as they appear in the noncommutative geometry approach to particle physics: in particular, the C*-algebras M n(R), Mn(C) and Mn(H), describing the finite noncommutative space of the Einstein-Yang-Mills systems, and the algebras A F = C H M3 (C) and Aev = H H M4(C), that appear in Chamseddine-Connes derivation of the Standard Model of particle physics coupled to gravity. As a byproduct, we identify a "free" version of the symplectic group Sp.n/ (quaternionic unitary group). PB - European Mathematical Society Publishing House UR - http://urania.sissa.it/xmlui/handle/1963/34897 U1 - 35182 U2 - Mathematics U4 - 1 ER -