Direct limit constructions in infinite-dimensional Lie theory

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Infinite-dimensional Lie groups are groups whose elements can be described by parameters in an infinite-dimensional vector space. They can be used to model symmetries of systems which depend on infinitely many parameters. Many infinite-dimensional Lie groups of interest can be expressed as a union G = UnN of subgroups G1  G2   which are easier to understand. For instance, each Gn might simply be a finite-dimensional Lie group (a situation which is now well understood). The current project is devoted to the more complicated case where already the pieces Gn are infinite-dimensional Lie groups. Its goals are to construct new classes of such groups; to explore their properties; and to obtain novel results concerning general direct limit groups Un Gn, beyond the specific examples.