''The Brothers Karamazov'' is a murder mystery, a courtroom drama, and an exploration of erotic rivalry in a series of triangular love affairs involving Karamazov and his three sons - the impulsive and sensual Dmitri; the coldly rational Ivan; and the healthy young novice Alyosha. Through the gripping events of their story, Dostoevsky portrays the social and spiritual strivings in what was both a golden age and a tragic turning point in Russian culture.