The radio galaxy Cen A has been detected all the way up to the TeV energy range. This raises the question about the dominant emission mechanisms in the high-energy domain. Spectral analysis allows us to put constraints on the possible emission processes. Here we study the hard X-ray emission as measured by INTEGRAL in the 3-1000 keV energy range, in order to distinguish between a thermal and non-thermal inverse Compton process. The hard X-ray spectrum of Cen A shows a significant cut-off at energies Ec = 434 (+106 -73) keV with an underlying power law of photon index 1.73 +- 0.02. A more physical model of thermal Comptonisation (compPS) gives a plasma temperature of kT = 206+-62 keV within the optically thin corona with Compton parameter y = 0.42 (+0.09 -0.06). The reflection component is significant at the 1.9 sigma level with R = 0.12 (+0.09 -0.10), and a reflection strength R>0.3 can be excluded on a 3 sigma level. Time resolved spectral studies show that the flux, absorption, and spectral slope varied in the range f(3-30 keV) = (1.2 - 9.2)e-10 erg/cm**2/s, NH = (7 - 16)e22 1/cm**2, and photon index 1.75 - 1.87. Extending the cut-off power law or the Comptonisation model to the gamma-ray range shows that they cannot account for the high-energy emission. On the other hand, also a broken or curved power law model can represent the data, therefore a non-thermal origin of the X-ray to GeV emission cannot be ruled out. The analysis of the SPI data provides no sign of significant emission from the radio lobes and gives a 3 sigma upper limit of f(40-1000 keV) < 0.0011 ph/cm**2/s. While gamma-rays, as detected by CGRO and Fermi, are caused by non-thermal (jet) processes, the main process in the hard X-ray emission of Cen A is still not unambiguously determined, being either dominated by thermal inverse Compton emission, or by non-thermal emission from the base of the jet.
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