Complex sentence: Antony's suspicions were apparently excited against lamblichus by his own brother Alexio I, who obtained the sovereignty after his brother's execution, but was shortly afterwards taken by Octavianus to Rome to grace his triumph, and then put to death.
Split into simpler sentences: Antony's suspicions were apparently excited against lamblichus by his own brother Alexio I, who obtained the sovereignty after his brother's execution. But Alexio was shortly afterwards taken by Octavianus to Rome to grace his triumph, and then put to death.