Geometry of the Gauge Algebra in Noncommutative Yang-Mills Theory

A detailed description of the infinite-dimensional Lie algebra of star-gauge transformations in noncommutative Yang-Mills theory is presented. Various descriptions of this algebra are given in terms of inner automorphisms of the underlying deformed algebra of functions on spacetime, of deformed symplectic diffeomorphisms, of the infinite unitary Lie algebra, and of the algebra of compact operators on a quantum mechanical Hilbert space. The spacetime and string interpretations are also elucidated.