Algae need nutrients like carbon, nitrogen, and phosphorus, among others, in order to grow. could carbon ever limit algae growth?

Carbon is abundant in the atmosphere and it will never be a limiting factor for the growth of algae. The limiting factors may be the presence of oxygen, other nutrients such as phosphorous, magnesium etc. But, if algae are growing at a very high rate in a water body, then carbon may be a limiting factor for its growth.