Complex sentence: After production of the trilogy's first volume began, Galás' brother, playwright Philip-Dimitri Galás, contracted HIV, which inspired the artist to redouble her efforts, resulting in the development of the aforementioned performance.
Split into simpler sentences: After production of the trilogy's first volume began, Galás' brother, playwright Philip-Dimitri Galás, contracted HIV. However, this tragic situation inspired the artist to redouble her efforts, resulting in the development of the aforementioned performance.