DANCE

Andris Liepa, a Bolshoi Ballet principal, will join American Ballet Theatre for the 1988-89 season, in New York and on tour, the company announced Monday. Liepa received special permission from the director of the Bolshoi Theatre and the Ministry of Culture for this new venture in international cultural exchange. Liepa, 25, the son of the great Bolshoi dramatic dancer Maris Liepa, was prominently cast in the 1987 Bolshoi tour of North America in “Romeo and Juliet,” “Giselle,” “Raymonda” and “The Golden Age.” Since then he has danced as a guest in this county with New York City Ballet and in other engagements on both coasts. His new, season-long relationship with Ballet Theatre will give him, he said, “the chance of dancing in America for an extended period of time and . . . the opportunity to dance new repertory that offers me an artistic challenge.”