There is a distinct relationship between al Arabi's concepts of Essence, Attributes, and Acts, and Gurdjieff's use of the terms essence and personality to describe man's state. the distinction, as I will demonstrate, is largely one of levels.
Al 'Arabi explains God as being composed of two different qualities: the Essence, which is forever incomparable and unknowable; and the Divinity, God in "His" or "Her" knowable form, in contact with material reality.
Although the Essence is irrevocably unknowable, the moment It emanates from Itself and creates material reality, It has altered its state (we might say, lowered Its rate of vibration, although this, like any other description, would not be quite correct) to create a knowable universe. In doing so, two parts of Itself interact intelligibly with the created universe.
The first of these parts is Acts, that is, things which have been created. The second part is Attributes, that is, aspects (al 'Arabi calles them names) of God which exert influences on the Acts. The three of them, together, create a holy Trinity directly analogous to the Father, the Son, and the Holy Spirit, or, in Gurdjieff's system, Holy Affirming, Holy Denying, and Holy Reconciling.
Although the dynamic nature of the teaching allows different elements to assume the same role, in the strictest sense, the right side of the enneagram always represents Holy Denying, the left Holy Affirming, and the transcendent note "do," from which all force within a given octave becomes manifest, Holy Reconciling.
All of what Gurdjieff referred to as personality occupies the outer portion of the diagram, that is to say, circulation around the perimeter, passage through the notes. Even though the notes actively exchange energy in an inner action, their visible manifestation always takes place in the realm of personality, that is, externally.
Two domains are created: one which can be known, that is, is redactable and subject to understanding through thought, whether or not said thought is classified as rational. (In this case, we include any form of sensory experience, including sensation and feeling, as thought.) This domain is the outer portion shaded in blue on the diagram.
The second domain, the light green shaded triangle, can never be known, although its influences are both vital and necessary. It is the domain of the Essence, the unknowable, and it occupies the inner triad which forms the support for the entire enneagram. The contact of the Essence with the knowable takes place in the locations Gurdjieff would have called conscious shocks, which, logically enough, represent Christ and the Holy Spirit in Christianity. We can deduce from this that this particular model encompasses Islamic, Christian, and Gurdjieffian understandings within a single diagram — in other words, the enneagram is able to perform its expected function of unifying apparently distinct bodies of knowledge under a single intelligible principle.
Gurdjieff frequently referred to essence and personality in his teachings. Because man, in his system, is a microcosmos who exactly reflects the metaphysical structure of the meta-cosmos, we should expect that his concepts of essence and personality translate to the meta-cosmic scale, and, in fact, they do. The understandings are similar enough that we can hypothesize Gurdjieff drew this portion of his teaching from Sufi understandings, and it is certainly plausible, furthermore, that he drew them from al 'Arabi himself, since it seems impossible he could have had the extensive contact with dervishes he indubitably had and not have encountered al 'Arabi's teachings on many occasions. Although his name is obscure to Western minds, it is anything but in Islam.
The question brings us to an interesting piece of territory, because the distinct nature of inner and outer work become evident in the picture of the diagram, and the nature of essence at its highest level raises some questions.
Inner work — the type of work which Gurdjieff (like Meister Eckhart) insisted was the only type of work that could affect a man's being — is understood, quite literally, in the context of this diagram and al 'Arabi's concepts of Essence and Divinity, as being a secret or Gnostic work. Secret in the sense that the work remains a work hidden even from the man himself, as he conducts it, because the work, in its absolute essence, is unknowable; it emanates from a domain that cannot be contacted by the known or the rational.
We certainly have enough allusions to this circumstance in Christ's teachings, which dovetail quite neatly into this picture. Esotericism, in other words, is not a secret work in which one person knows the secrets, and another person does not; it's a secret work in which the secrets cannot be known. Only their effects can be known: and they emanate from a mystery that can never be penetrated by Being, even though Being owes its existence to them.
I respectfully hope you will take good care.