Fade in UV lights connected to mains
Most LED lights can't be dimmed from the mains supply.

In order to dim LEDs you have 2 choices: Limit the current through each LED or series string of LEDs, or pulse them very rapidly with a varying ratio of on/off times (known as a variable "duty cycle")

It's usually easiest to pulse them. To do that you need to be able to control the flow of DC to the LED array. If you were to take apart your IR array you would very likely find an AC to DC power supply that then feeds the LEDs through current limiting resistors.

If you can figure out the voltage and current that comes out of the DC power supply, you can select a power transistor (almost certainly a logic level power MOSFET) to wire in as an electronic switch that enables you to pulse the power to the LEDs using a logic signal from your Arduino.

This is actually a lot simpler than it sounds. You would cut 1 wire inside your LED array, solder in a single transistor to the 2 ends of the cut wire, and run the third wire from the transistor out to your Arduino.

Arduinos have several I/O lines that can be configured for PWM (Pulse Width Modulation) which is designed for this very purpose. You'd connect a PWM line to the gate of a logic level power MOSFET, and then send it a signal from 0 to 255, which would effectively dim the LED array in 255 brightness steps.

There are beginner sample projects that let you dim single visible light LEDs using this very approach. (For a single LED you don't need a transistor though, so they are really easy to wire up. All you need is a current limiting resistor.) I suggest you find and build one of those projects to get a feel for how (and how well) it works.