Who is the Waliy (a legal guardian representing the bride) of a half-sister, the brother or the maternal uncle?
Is it permissible for her mother to give her in marriage without the knowledge of her brother?
If the case is as you have mentioned, her Waliy will be her paternal brother. Her mother is not permitted to act as her Waliy in marriage. As for the maternal uncle, he is not Waliy as he is not an paternal relative. (Part No. 18; Page No. 153) May Allah grant us success. May peace and blessings be upon our Prophet, his family and Companions.