Photosynthesis is the process of using light to process minerals to produce enegry.
pho·to·syn·the·sis (fō'tō-sĭn'thĭ-sĭs)
n. The process in green plants and certain other organisms by which carbohydrates are synthesized from carbon dioxide and water using light as an energy source. Most forms of photosynthesis release oxygen as a byproduct.
Source: Dictionary.com
Light is the catalyst, but the other nutrients need to be present. Ill get more info if needed, however, from personal experience from environmental science I can assure you that other minerals need to be present for algae to grow.
To answer the question of the never ending cycle of die off creating the minerals to support more growth. Algae uses more nutrients to grow then is expelled during decomp.
Tap water contains nitrates and phosphates and a bunch of other crap we probably shouldnt be drinking. lol. i just happens to be a perfect blemd for algae.
We use RODI water to keep these out our tank, and anyone that has switched over will tell you that it helps eliminate and prevent algae growth.