The classifying space of a bound quiver

We associate to a bound quiver (Q,I) a CW-complex which we denote by B(Q,I), and call the classifying space of (Q,I). We show that the fundamental group of B(Q,I) is isomorphic to the fundamental group of (Q,I). Moreover, we show that this construction behaves well with respect to coverings. On the other hand, we study the (co)homology groups of B(Q,I), and compare them with the simplicial and the Hochschild (co)homology groups of the algebra A=kQ/I. More precisely, we give sufficient conditions for these groups to be isomorphic. This generalizes a theorem due to Gerstenhaber and Schack.Comment: Revised version. To appear in J. Algebra. 22 pages, 3 postscript figure

Light flavour hadron production in pp collisions at s\sqrt{s} = 13 TeV with ALICE

The ALICE detector has excellent Particle IDentification (PID) capabilities in the central barrel ($\lvert \eta \rvert <$ 0.9). This allows identified hadron production to be measured over a wide transverse momentum ($p_{\rm{T}}$) range, using different sub-detectors and techniques: their specific energy loss (d$E$/d$x$), the velocity determination via time-of-flight measurement, the Cherenkov angle or their characteristic weak decay topology. Results on identified light flavour hadron production at mid-rapidity measured by ALICE in proton-proton collisions at $\sqrt{s}$ = 13 TeV are presented and compared with previous measurements performed at lower energies. The results cover a wide range of particle species including long-lived hadrons, resonances and multi-strange baryons over the $p_{\rm{T}}$ range from 150 MeV/$c$ up to 20 GeV/$c$, depending on the particle species.Comment: 4 pages, 4 figures, Proceedings of Hot Quarks September 12-17, 2016, South Padre Island, Texas, US