We present observations of a giant Lyman-alpha blob in the SSA22 proto-cluster at z=3.1, SSA22-LAB1, taken with the Atacama Large Millimeter/submillimeter Array (ALMA). Dust continuum, along with [C II]158um, and CO(4-3) line emission have been detected in LAB1, showing complex morphology and kinematics across a ~100 kpc central region. Seven galaxies at z=3.0987-3.1016 in the surroundings are identified in [C II] and dust continuum emission, with two of them potential companions or tidal structures associated with the most massive galaxies. Spatially resolved [C II] and infrared luminosity ratios for the widely distributed media (L[C II]/LIR~0.01-0.001) suggest that the observed extended interstellar media are likely to have originated from star-formation activity and the contribution from shocked gas is probably not dominant. LAB1 is found to harbour a total molecular gas mass Mmol=(8.7+/-2.0)e+10 Msun, concentrated in the core region of the Ly-alpha-emitting area. While (primarily obscured) star-formation activity in the LAB1 core is one of the most plausible power sources for the Ly-alpha emission, multiple major-mergers found in the core may also play a role in making LAB1 exceptionally bright and extended in Ly-alpha as a result of cooling radiation induced by gravitational interactions.
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