Bioluminescence is badass. It involves living beings emitting bright light in the visible spectrum.
Would it be, though, possible that a lifeform emits UV (ultraviolet) light? Does it occur in reality, maybe?
What are the requirements for it to happen?
With regards to the real-world, the NOAA says that some deep-sea crabs have low-level UV sensitivity in certain pigments. This would seem to indicate that creatures there may emit UV light - which is exactly what you're looking for - potentially as a form of communication1:
In addition, data obtained on previous OE-funded expeditions indicate that the deep-sea benthos may produce novel, short wavelength bioluminescence. During Deep Scope 2005, we discovered that several species of the deep-sea crabs (figure 2b) have an ultraviolet (UV)-sensitive visual pigment in addition to a blue-sensitive one. In their dim light environment, sacrificing room in their eyes for a UV visual pigment suggests that UV sensitivity plays an important role in their ecology. Just as unusual UV sensitivity in several deep-sea pelagic species has been linked to bioluminescence, we suspect that UV sensitivity may also function to see as-yet-undiscovered short wavelength bioluminescence from benthic organisms. UV bioluminescence in the benthos may be a novel private channel of communication, allowing these animals to find their preferred habitat.
Additionally, Photophysiology: Action of Light on Animals and Microorganisms; Photobiochemical Mechanisms; Bioluminescence cites the findings of Cormier and Eckroade (1962) of evidence of bioluminescent emission in the UV wavelengths in three species of the Renilla genus (commonly called sea pansies; these effects were later investigated by Hart et al. (1979)). It's important to note that the emission of photons in UV wavelengths is only due to a "tailing off" of the spectral energy distribution in the bioluminescence of these species.
Feasibility is more complicated. The mechanism2 is $$\text{L}+\text{O}_2+\text{ATP}\to\text{oxy-L}+\text{CO}_2+\text{AMP}+\text{PP}+\text{light}$$ as mediated by the enzyme luciferase using one of the luciferin pigments. Essentially, the luciferin changes from an excited state to a ground state. Now, we can postulate the existence of a luciferin with an energy difference between these two states exactly right to produce one or more UV photons; in fact, Biology: The Unity and Diversity of Life claims that "some even emit ultraviolet or infrared light" but doesn't specify which luciferins it is referencing.
1 UV light is used for communication in other animals; see Sensory Ecology, Behavior, and Evolution.
2 Note that this is not the only reaction mechanism for bioluminescence.
