@article {2014,
title = {Quantum gauge symmetries in noncommutative geometry},
number = {Journal of Noncommutative Geometry;volume 8; issue 2; pages 433-471;},
year = {2014},
publisher = {European Mathematical Society Publishing House},
abstract = {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).},
doi = {10.4171/JNCG/161},
url = {http://urania.sissa.it/xmlui/handle/1963/34897},
author = {Jyotishman Bhowmick and Francesco D{\textquoteright}Andrea and Biswarup Krishna Das and Ludwik Dabrowski}
}
@article {2011,
title = {Quantum Isometries of the finite noncommutative geometry of the Standard Model},
journal = {Commun. Math. Phys. 307:101-131, 2011},
number = {arXiv:1009.2850;},
year = {2011},
publisher = {Springer},
abstract = {We compute the quantum isometry group of the finite noncommutative geometry F describing the internal degrees of freedom in the Standard Model of particle physics. We show that this provides genuine quantum symmetries of the spectral triple corresponding to M x F where M is a compact spin manifold. We also prove that the bosonic and fermionic part of the spectral action are preserved by these symmetries.},
doi = {10.1007/s00220-011-1301-2},
url = {http://hdl.handle.net/1963/4906},
author = {Jyotishman Bhowmick and Francesco D{\textquoteright}Andrea and Ludwik Dabrowski}
}
@article {2003,
title = {Quantum spin coverings and statistics},
journal = {J. Phys. A 36 (2003), no. 13, 3829-3840},
number = {SISSA;97/2002/FM},
year = {2003},
publisher = {IOP Publishing},
abstract = {SL_q(2) at odd roots of unity q^l =1 is studied as a quantum cover of the complex rotation group SO(3,C), in terms of the associated Hopf algebras of (quantum) polynomial functions. We work out the irreducible corepresentations, the decomposition of their tensor products and a coquasitriangular structure, with the associated braiding (or statistics). As an example, the case l=3 is discussed in detail.},
doi = {10.1088/0305-4470/36/13/314},
url = {http://hdl.handle.net/1963/1667},
author = {Ludwik Dabrowski and Cesare Reina}
}