There is a imperial cult after Augustus' reign, and the augustan deities remain being worshiped after his death. Exactly what kind relationship between these worships and Augustus?
From memory, Augustus shied away from divine honours in his own life time. Julius Caesar had been given divine honours in 42 BCE, not long after his assassination. The apotheosis was part of a range of measures that included making all of Caesar's acts binding, as part of a consolidation of the authority of the 2nd Triumvirate. But the characterisation of Octavian as the son of the divine Julius did little to enhance his influence, power or authority at that time.
Augustus was heavily lobbied by sectors of the eastern empire who wanted to be allowed to worship him as a god. This arising both from simple flattery and the experience of past Hellenistic rulers to present themselves as gods. The Ptolemies of Egypt are a good example.
Augustus' chose to resolve the problem with the kind of practical compromise that was his hallmark. While he was alive it was not permitted to worship him as a God, but temples could be dedicated to Rome and the Spirit of Augustus. Thereby binding himself and his authority to that of Rome itself.
After his death, Tiberius had Augustus deified. Tiberius himself was not. Gaius (Caligula) made some claim at divinity but was assassinated, not just for that. Claudius deified Augustus' wife Livia, and was himself deified by Nero. But the routine elevation of emperors to the ranks of the divine was not automatic in the first century of the Principate.
A very interesting article, Helene. Would certainly recommend it. Technically, I should have referred to the Genius of Augustus, rather than Spirit. Scullard's comments pp. 242 - 243 in From the Gracchi to Nero, could also be helpful, Paulo.