No, blue-green algae, also known as cyanobacteria, are generally not parasites.
While the reference mentions that some algae of certain genera are parasitic, it's crucial to understand that blue-green algae (cyanobacteria) are distinct from green algae. Cyanobacteria are prokaryotic organisms, meaning they lack a membrane-bound nucleus and other complex organelles. True algae, including green algae, are eukaryotic. This fundamental difference impacts their modes of nutrition and interaction with other organisms.
Therefore, even though some green algae can be parasitic, this information does not apply to blue-green algae (cyanobacteria). Cyanobacteria are typically free-living and photosynthetic, meaning they produce their own food from sunlight. Some can form symbiotic relationships, but parasitism is not their primary mode of survival.