SUPERSYMMETRY ALGEBRA IN N=1 CHIRAL SUPERGRAVITY

We consider the supersymmetry (SUSY) transformations in the chiral Lag rangian for N = 1 supergravity (SUGRA) with a complex tetrad following the method used in the usual N = 1 SUGRA, and present the explicit fo rm of the SUSY transformations in the first-order form. The SUSY trans formations are generated by two independent Majorana spinor parameters , which are apparently different from the constrained parameters emplo yed in the method of the two-form gravity. We also calculate the commu tator algebra of the SUSY transformations on shell.