Thomas Cavalier-Smith proposed in 2004 the Chromist Kingdom, which is currently considered one of the six kingdoms of living beings.
It was the old kingdom Stramenopila (which in the 1990s was one of the three divisions of the Fungi Kingdom).
This kingdom encompasses several groups of algae. They are eukaryotic organisms (have the nucleus structures separated from the others by a membrane) and have the presence of flagella, which can be multicellular or unicellular.
As for food, beings in this realm may be autotrophs, heterotrophic, and others are photosynthesizers. The latter acquire chloroplasts by endosymbiosis (the relationship in which one organism lives inside the other's body without harming it) with red algae.