  High dimensional expanders is a vibrant emerging field of study.
Nevertheless, the only known construction of bounded degree high dimensional
expanders is based on Ramanujan complexes, whereas one dimensional bounded
degree expanders are abundant.
  In this work, we construct new families of bounded degree high dimensional
expanders obeying the local spectral expansion property. This property has a
number of important consequences, including geometric overlapping, fast mixing
of high dimensional random walks, agreement testing and agreement expansion.
Our construction also yields new families of expander graphs which are close to
the Ramanujan bound, i.e., their spectral gap is close to optimal.
  The construction is quite elementary and it is presented in a self contained
manner; This is in contrary to the highly involved previously known
construction of the Ramanujan complexes. The construction is also very
symmetric (such symmetry properties are not known for Ramanujan complexes) ;
The symmetry of the construction could be used, for example, in order to obtain
good symmetric LDPC codes that were previously based on Ramanujan graphs.
  The main tool that we use for is the theory of coset geometries. Coset
geometries arose as a tool for studying finite simple groups. Here, we show
that coset geometries arise in a very natural manner for groups of elementary
matrices over any finitely generated algebra over a commutative unital ring. In
other words, we show that such groups act simply transitively on the top
dimensional face of a pure, partite, clique complex.
