What roles did the Shi'a variant of Islam play in the rise of the Safavid dynasty and the state, society, and artistic expression that flourished in Persia under its rule?

The Safavid Empire was a theocracy and Shi'a was the state religion, other forms of religion were suppressed. The Safavids spent money to promote their religions, they made grants to shrines and built religious schools. They gave lands and money to create a new class of religious aristocrats. Because of their geographical position, they were in the center of trade routes and this way they would become rich because of the trade between Europe and the Islamic civilizations, this way they promoted their art - tile making, pottery, textiles - were sold.

There was also a huge advance in philosophy with the foundation of The Isfahan School, in medicine - books on pharmacology were written such as the "Pharmacopoea Persica".