The show, whose varied score ranges from pop ballads to sexy R&B to rap battles, is nominated in 13 categories, including best new musical. Jamael Westman, in the title role, and Giles Terera as Aaron Burr are both nominated for best actor in a musical.
Other contenders for an Olivier in acting include Bryan Cranston for "Network," Andrew Garfield for "Angels in America" and Imelda Staunton, nominated for both "Follies" and "Who's Afraid of Virginia Woolf?"
Jez Butterworth's Northern Ireland drama "The Ferryman" has eight nominations in non-musical categories. The awards will be handed out on April 8.