There are 4 elements that correspond to the 4 letters of Havayah:
Paralleling the first yud of Havayah is the element of water - Abraham - chesed - South
Paralleling the hei of Havayah is element of fire - Isaac - harsh gevura - North
Paralleling the vav of Havayah is the element of air - Jacob - tiferet - East
Paralleling the final hei of Havayah is the element of dust/earth - David - lower Sefira (i.e. soft) gevura [malchut] - West.
The first hei, paralleling Isaac, is harsh judgment. It is for this reason that it [this hei] appears twice in the Havayah. For the milui ["spelling out"] of this letter is hei-hei. That is, [before the second hei is emanated as a separate power], it is merely the milui of the first hei. It [didn't exist as a separate concept until it] emerged from [its state of concealment within] the first hei.
This World was created with this smaller [second] hei. It is for this reason that the letter hei in the word "be'hi'bar'am" - "…when they were created" (Gen. 2:4) is written small.
The phrase can also be interpreted: "in [the letter] hei He created them."
For, just as the milui is not recognizable [as a separate letter] when we pronounce a letter, so also, in this milui, hei is subsumed in the first hei.
Essentially, Havayah has three main letters. The lower hei, corresponding to Earth, emerged from the first hei, corresponding to Fire…
Correspondingly, the four elements are really only three: water, fire and air. For, similar to ash [in Hebrew, "efer"], the element of Earth [in Hebrew, "afar" - like "efer"] is what is left over after having been burned by fire. So also [in the spiritual root], the lower hei, corresponding to Earth, emerged from the first hei, corresponding to Fire.
Corresponding to the 4 letters of Havayah, G‑d also brought forth 4 worlds [universes, dimensions]: ABY"A [Atzilut, Beriya, Yetzira, Asiya]. The intention in this was as follows: [Based on the analogy of the sun as the source of energy for our solar system,] the Blessed Ein Sof Himself, as the Ultimate Spiritual Energy Source, could make a material world only by creating enormous distance. Only when He emerges to sit on His throne and govern His kingdom does He reveal Himself…
Now, behold, in the dimension of Atzilut, there is no angel [of Yetzira] or Seraph [of Beriya]. There is only His Name. This can be likened to a king who sits alone [invisible] in his innermost chamber. Only when He emerges [from his concealment] to sit on His throne and govern His kingdom does He reveal Himself to His princes and servants.
[The king in his innermost chamber is the level of Atzilut. The throne is the level of Beriya.] The princes are the level of Yetzira. The servants are the level of Asiya and all that is below them.
The fact that He is called by a name [Havayah] in Atzilut already suggests a degree of limitation. Above Atzilut, even this is forbidden.
According to the Kabbala, even the name Havayah is a limitation for He Who Is Beyond Any Name and/or Appellation. Kabbala emphasizes that none of the names with which the Torah describes G‑d's interaction with us refer to G‑d Himself. No, G‑d Himself, for Whom even the appellation Ein Sof (Endless One) is a limitation, Is Beyond All Name and/or Description. G‑d's names refer to the various ways He runs His universe and relates to us…
Rather, G‑d's names refer to the various ways He runs His universe and relates to us. Look at any verse in Scripture in which any of the Divine Names appear. According to Kabbala, none of these Names refer to G‑d Himself in any literal sense. That possibility simply does not exist by virtue of the rule that G‑d Is Beyond All Names.
Nevertheless, relative to all other divine names, the name Havayah is the root. The reason for this might be that Havayah is not just a name, but a four-letter formula: yud, hei, vav and hei. As the Kabbala teaches, this four-letter formula includes all divine names and modes in a total unity. All other divine names are derivatives and specific aspects of this all-encompassing name.
Paralleling the universe of Atzilut, G‑d thus said, "All was called [into existence] for My Name's sake" (Isaiah 43:7). In Atzilut, it is possible to call Him by Name.
The entire verse reads: "All was called [into existence] for My Name's sake. For My Glory I have created it, I have formed it, and I have also completed it" (Isaiah 43:7). According to the way the Rav is reading it now, this verse speaks about the 4 worlds:
Atzilut: "All was called [into existence] for My Name's sake."
Beriya: " For My Glory I have created it…."
Yetzira: "…I have formed it…"
Asiya: "…I have also completed it."
After Atzilut, He created the universe of Beriya, which is called "World of the Throne". It is there that He reveals Himself by way of "Hht'lab'shut" [i.e. the higher, ethereal level "clothing itself" in the lower level]. This is the idea of the throne being His "glory", similar to the way Rabbi Yochanan called his garments "my glory". This is why the verse says, "For My Glory I have created it."
Now, if the world of Beriya would desire to exceed its own domain, by rising up and entering into [or crossing the boundary between it and] the domain of Atzilut, it would immediately be nullified and burnt [and cease to exist as a separate dimension; rather it would be subsumed in the higher dimension from which it emerged]. It cannot exist except in its own domain.
The same is true of Yetzira. If it would come too close to [the boundary of] Beriya, it would be burnt and nullified. This is why the verse states, "I have formed it."
Regarding the world of Asiya, it then says, "I have also completed it." If His 'word' were too revealed, it would have been impossible to bring a physical world into existence…
Clearly, the intention of emanating these 4 worlds was in order to hide Himself in one garment after another, so that creatures in this lowest world could exist. This is the meaning of the verses, "It is G‑d's honor to hide a 'davar' [which can be translated as 'thing' or 'word']" (Proverbs 25:2), for "With the 'word' of G‑d the heavens were made". If His "word" were too revealed, it would have been impossible to bring a physical world into existence. Only by concealing and hiding [the light], namely, the concealment of His words in garment after garment, can the worlds be made and continue to exist.
And so it is with all created things in the world. Their names in the Holy Tongue [Hebrew] are the very letters of G‑d's 'speech' that descend, level by level, from the Ten Utterances of Creation recorded in the Torah, by means of substitutions and transpositions of letters through the 231 Gates [of permutations], until they reach down and become clothed in that particular created entity. [This gradual descent is necessary] because individual creatures are simply incapable of receiving their life-force directly from the Ten Utterances of the Torah, for the life-force issuing directly from them is far greater than the capacity of individual creatures to receive. They can only receive it when it descends and [its power] is progressively diminished, step by step... until it can be condensed and clothed [in a lower form], and finally bring into existence an individual creature. The name that that creature is then called in the Holy Tongue is a conduit for the life-force that is condensed into its letters....[Shaar Ha'yichud Ve'ha'emunah, chap. 1, p. 77a by Rabbi Shneur Zalman of Liadi]
This is like fire that consumes everything that comes into close proximity with it. There are certain things, like stones, that can come close, and not be burnt immediately. On the other hand, straw and stubble would be burnt on the spot. However, if the straw and stubble are removed from the immediate vicinity of the fire, they will not be burned on the spot.
[Translated and adapted by Avraham Sutton from Likutei Torah, Parashat Bereishit (Chumash HaAri, Bereishit, p. 7-9)]