  Supersymmetric gauge theories of certain class possess a large hidden
nonperturbative symmetry described by the Ding-Iohara-Miki (DIM) algebra which
can be used to compute their partition functions and correlators very
efficiently. We lift the DIM-algebraic approach developed to study holomorphic
blocks of 3d linear quiver gauge theories one dimension higher. We employ an
algebraic construction in which the underlying trigonometric DIM algebra is
elliptically deformed, and an alternative geometric approach motivated by
topological string theory. We demonstrate the equivalence of these two methods,
and motivated by this, prove that elliptic DIM algebra is isomorphic to the
direct sum of a trigonometric DIM algebra and an additional Heisenberg algebra.
