  We study Quantum Many-Body Scars (QMBS) in the language of commutant
algebras, which are defined as symmetry algebras of families of local
Hamiltonians. This framework explains the origin of dynamically disconnected
subspaces seen in models with exact QMBS, i.e., the large "thermal" subspace
and the small "non-thermal" subspace, which are attributed to the existence of
unconventional non-local conserved quantities in the commutant; hence this
unifies the study of conventional symmetries and weak ergodicity breaking
phenomena into a single framework. Furthermore, this language enables us to use
the von Neumann Double Commutant Theorem (DCT) to formally write down the
exhaustive algebra of all Hamiltonians with a desired set of QMBS, which
demonstrates that QMBS survive under large classes of local perturbations. We
illustrate this using several standard examples of QMBS, including the spin-1/2
ferromagnetic, AKLT, spin-1 XY $\pi$-bimagnon, and the electronic
$\eta$-pairing towers of states; and in each of these cases we explicitly write
down a set of generators for the full algebra of Hamiltonians with these
QMBS.Understanding this hidden structure in QMBS Hamiltonians also allows us to
recover results of previous "brute-force" numerical searches for such
Hamiltonians. In addition, this language clearly demonstrates the equivalence
of several unified formalisms for QMBS proposed in the literature, and also
illustrates the connection between two apparently distinct classes of QMBS
Hamiltonians -- those that are captured by the so-called Shiraishi-Mori
construction, and those that lie beyond. Finally, we show that this framework
motivates a precise definition for QMBS that automatically implies that they
violate the conventional Eigenstate Thermalization Hypothesis (ETH), and we
discuss its implications to dynamics.
