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?

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    Does this answer your question? “Das ist sein Pass.“ Is this sentence right? – David Vogt Jan 12 '20 at 9:11
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    Just noting that this is ontopic here. If op has confused the cases, then a conjugation table doesn't help. – infinitezero Jan 12 '20 at 11:02
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    I'd be surprised if in any language the "object of the to be verb" would be a direct object, thus I don't see why this is related to German. – c.p. Jan 12 '20 at 21:01
  • I agree with @infinitezero - this question should have been closed as duplicate instead. – Volker Landgraf Jan 13 '20 at 10:12
  • I also agree that the question should have been closed as a duplicate...I'll flag the moderators. – Guillermo Mosse Jan 13 '20 at 17:56

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.

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