Your planet is a bit warmer than Earth
Okay, so just being warmer alone will not give you a violet sky, but it does two really important things. It will increase the amount of water vapor in the air and it will make the polar regions the primary habitable zone of the world since the tropics will be too hot for any Earthlings. Purple skies here on Earth are caused by the way light scatters when our yellow sunlight hits a sky full of a combination of gaseous and crystalline water in the air at an acute angle.
Here Here on Earth, our poles get a perpetual twilight that typically looks like this:
Because of how cold the air is you don't get a lot of water vapor to scatter the light, but if the poles had a temperate environment, it would look more like this for the 6 months of the year that you get sunlight:
Purple skies here on Earth are caused by the way light scatters when sunlight hits a sky full of water vapor and other "large" particulates (aka: clouds) in the air at an acute angle. The acute angle causes the sunlight to scatter via the Tyndal effect such that the blue wavelengths are filtered out before they reach the sky overhead leaving only light in the red spectrum to illuminate you and any cloud cover. So we get red clouds and a generally pinkish ambiance. However, the sky above the clouds has smaller particulates; so, it is not effected by the Tyndal effect. Its primary mode of light refraction comes from Rayleigh scattering which means that the sky above the clouds will appear blue. So, even though you have 1 light source, its light is being filtered differently at different layers of the atmosphere causing the light reaching you to be mostly blue and red with very little in the green range giving the sky a violet hue.
Technically speaking, this world would still have generally blue/white or maybe even entirely white sky at lower latitudes, but in the regions that people could safely call home, ita purple sky would be all purple all the timenorm.
This could even be Humanity's actual future here on Earth
If the runaway greenhouse effect goes as predicted, then we may not actually need to go to another planet for our decedents to eventually experience this. As global temperatures rise from greenhouse emissions, an increase in atmospheric water vapor will go hand in hand with the increase in atmospheric CO2. The poles of Earth will become increasingly humid while the tropics become barren wastelands. Eventually more humans may live under a violet sky than a blue one as we flee to the only remaining habitable parts of the planet.