  In this paper, we are going to discuss the gauge reduction with respect to
the simplicity constraint in both classical and quantum theory of all
dimensional loop quantum gravity. With the gauge reduction with respect to
edge-simplicity constraint being proceeded and the anomalous vertex simplicity
constraint being imposed weakly in holonomy-flux phase space, the simplicity
reduced holonomy can be established. However, we find that the simplicity
reduced holonomy can not capture the degrees of freedom of intrinsic curvature,
which leads that it fails to construct a correct scalar constraint operator in
all dimensional LQG following the standard strategy. To tackle this problem, we
establish a new type of holonomy corresponding to the simplicity reduced
connection, which captures the degrees of freedom of both intrinsic and
extrinsic curvature properly. Based on this new type of holonomy, we propose
three new strategies to construct the scalar constraint operators, which serve
as valuable candidates to study the dynamics of all dimensional LQG in the
future.

General Relativity and Quantum Cosmology