yes some can be purple
Purple Bhut Jolokia, Fidalga Roxa,Pitanga Morango,Pimenta Do Nayde and CGN 21500 are purple and are Chinense species, this only to name a few, these listed above are naturally purple from the start and stay purple as long as they get plenty of light
so yeah they can be purple
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Hops and Barley is also correct the purple can be a response to too much bright direct light (sort of on the order of a suntan if you will)
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hope this helps
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thanks your friend Joe