With my translation tools / online courses I see that the phrase "Luke, ich bin dein Vater" is correct. However, I do not understand why we shouldn't use "deinen". Isn't Darth Vader the direct object of the sentence? Isn't this an example of the accusative case?
It is correct to make a difference between possessive pronouns and possessive determiners (articles). But for "ich bin dein Vater" (which is correct) the point is, that the complements of the verb "sein" are not the subject (nominative) and an accusative object (as for haben, nehmen, kennen and most of the verbs). "Sein" has a subject and a predicative complement, and both of them are nominative, as in
Er ist ein guter Fahrer.