We analyse the stellar kinematics of the z=0.169 brightest cluster galaxy (BCG) in Abell 1201, using integral field observations with VLT/MUSE. This galaxy has a gravitationally-lensed arc located at unusually small radius ($sim$5 kpc), allowing us to constrain the mass distribution using lensing and stellar dynamical information over the same radial range. We measure a velocity dispersion profile which is nearly flat at $sigma$ $approx$ 285 km/s in the inner $sim$5 kpc, and then rises steadily to $sigma$ $approx$ 360 km/s at $sim$30 kpc. We analyse the kinematics using axisymmetric Jeans models, finding that the data require both a significant dark matter halo (to fit the rising outer profile) and a compact central component, with mass $M_{rm cen}$ $approx$ 2.5$times$10$^{10}$ $M_odot$ (to fit the flat {sigma} in the inner regions). The latter component could represent a super-massive black hole, in which case it would be among the largest known to date. Alternatively $M_{rm cen}$ could describe excess mass associated with a gradient in the stellar mass-to-light ratio. Imposing a standard NFW dark matter density profile, we recover a stellar mass-to-light ratio $Upsilon$ which is consistent with a Milky-Way-like initial mass function (IMF). By anchoring the models using the lensing mass constraint, we break the degeneracy between $Upsilon$ and the inner slope $gamma$ of the dark matter profile, finding $gamma$=1.0$pm$0.1, consistent with the NFW form. We show that our results are quite sensitive to the treatment of the central mass in the models. Neglecting $M_{rm cen}$ biases the results towards both a heavier-than-Salpeter IMF and a shallower-than-NFW dark matter slope ($gamma$ $approx$ 0.5).
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