gvalued
G-valued is an adjective used in mathematics and theoretical physics to denote that a given object takes its values in a Lie algebra g associated with a Lie group G. This convention appears in differential geometry, gauge theory, and representation theory. When fields or forms are defined on a manifold, a g-valued object assigns to each point an element of g rather than a real number or a vector space.
In notation, g typically denotes Lie(G). A g-valued differential form on a manifold M is a form
In gauge theory, the connection form is g-valued, and its curvature is a g-valued 2-form. The theory
Notes: The term is context-dependent and describes the codomain or target of a field, form, or map,