Direct limit constructions in infinite-dimensional Lie theory

• Applicant: Professor Dr. Helge Glöckner
• Subject Area: Mathematics
• Term: from 2007 to 2011
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 50049100

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.

• DFG Programme: Research Grants