Invertible subalgebras

Understand

We introduce invertible subalgebras of local operator algebras on lattices.

• An invertible subalgebra is defined to be one such that every local operator can be locally expressed by elements of the inveritible subalgebra and those of the commutant.
• On a two-dimensional lattice, an invertible subalgebra hosts a chiral anyon theory by a commuting Hamiltonian, which is believed not to be possible on any full local operator algebra.
• We prove that the stable equivalence classes of $\mathsf d$-dimensional invertible subalgebras form an abelian group under tensor product, isomorphic to the group of all $\mathsf d + 1$ dimensional QCA modulo blending equivalence and shifts.