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Basically it has to do with the blackbody spectrum.

Hot objects emit a broad spectrum of light, not just a single color. At the point where the temperature is such that the blackbody radiation peaks in the ultraviolet the overall spectrum is such that the emitted light appears to us as largely blue.

There may well be purple stars, but from our eyes, they appear blue. Our eyes, slightly deceive us.

See the related link for a picture of how our eyes perceive colour at a given temperature, and another for a video explaining in detail this question.

Our Sun would appear a kind of peach, if we had eye's better developed to a blackbody spectrum

Purple is a combination of blue and red. The light emitted by a star is of such a nature (black body radiation curve) that there is one predominate colour and lesser component of lower frequencies. (Higher frequencies are rapidly attenuated.) It is therefore impossible to get two colour emission peaks in both the blue and red of equal intensity - consequently no purple stars.

However you could have two stars closely orbiting each other: one blue and the other a red super giant, that at a great distance would look like a purple star, or a red star with a super hot white dwarf, that would work too. Interesting to note, the star Algol might fulfill this combination.

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