ALMA observations of the Galactic center with spatial resolution 2.61 ^ { \prime \prime } \times 0.97 ^ { \prime \prime } resulted in the detection of 11 SiO ( 5-4 ) clumps of molecular gas within 0.6pc ( 15 ^ { \prime \prime } ) of Sgr A* , interior to the 2-pc circumnuclear molecular ring . The three SiO ( 5-4 ) clumps closest to Sgr A* show the largest central velocities , \sim 150 km s ^ { -1 } , and broadest asymmetric linewidths with full width zero intensity ( FWZI ) \sim 110 - 147 km s ^ { -1 } . The remaining clumps , distributed mainly to the NE of the ionized mini-spiral , have narrow FWZI ( \sim 18 - 56 km s ^ { -1 } ) . Using CARMA SiO ( 2-1 ) data , LVG modeling of the the SiO line ratios for the broad velocity clumps , constrains the column density N ( SiO ) \sim 10 ^ { 14 } cm ^ { -2 } , and the H _ { 2 } gas density n _ { H _ { 2 } } = ( 3 - 9 ) \times 10 ^ { 5 } cm ^ { -3 } for an assumed kinetic temperature 100-200K . The SiO clumps are interpreted as highly embedded protostellar outflows , signifying an early stage of massive star formation near Sgr A* in the last 10 ^ { 4 } -10 ^ { 5 } years . Support for this interpretation is provided by the SiO ( 5-4 ) line luminosities and velocity widths which lie in the range measured for protostellar outflows in star forming regions in the Galaxy . Furthermore , SED modeling of stellar sources shows two YSO candidates near SiO clumps , supporting in-situ star formation near Sgr A* . We discuss the nature of star formation where the gravitational potential of the black hole dominates . In particular , we suggest that external radiative pressure exerted on self-shielded molecular clouds enhances the gas density , before the gas cloud become gravitationally unstable near Sgr A* . Alternatively , collisions between clumps in the ring may trigger gravitational collapse .