What must I do after I swore: "By the life of the Qur'an, you will not sleep in the house," and my brother slept in the house?

It is permissible to swear by the Quran because it is the word of Allah and one of His attributes. If one swears by "the life of the Quran," it carries the same ruling. Whoever swore to his brother that he would not sleep in the house, and he slept, then he must offer expiation for breaking an oath. If the oath was concerning abandonment and estrangement, then he should break his oath and offer expiation for it, because that is better.