The new battery on my Craftsman LT1000 18hp riding mower will not charge. Anyone have any ideas?

If you replace the Battery and it does not charge you need to test the stator or as I call it the alternator with a multitester.the stator is located underneathe the fan\flywheel and requires a fly wheel puller to pull off fly wheel and to bolt new stator underneath.but i would test it with a multi meter.they are about 50 new.you will see the red wire for stator coming out of engine aboutr midway down unplug it and test it.
Set the multi-tester dial to AC VOLTS or DC AMPS.
Insert the black multi-tester lead into the tester's COM receptacle.

• For AC VOLTS, connect the other end to ground, such as an engine bolt or cylinder fin.
• For DC AMPS, connect the other end to the battery's positive terminal. (NOTE: The battery must be grounded to the equipment frame of the engine block to create a complete circuit.)

Ck for blown fuse, ck for broken wire.