Project Details
Projekt Print View

Self-similar groups and algebras

Subject Area Mathematics
Term from 2010 to 2017
Project identifier Deutsche Forschungsgemeinschaft (DFG) - Project number 179753345
 
Self-similar, or fractal, objects abound in geometry, but their impact on algebra is relatively new. Groups, associative algebras, and Lie algebras are called self-similar if they are equipped with a biset (respectively bimodule), namely a set (resp. module) with commuting left and right actions, which is free qua right set (resp. module). Important examples include the infinite torsion groups, and groups of exponential growth, by Grigorchuk inter alia. A dynamical system may be conveniently encoded as a self-similar group; this yields an extremely potent algebraic invariant of that dynamical system, and a link between dynamics and algebra.The proposal will concentrate on two major aspects of self-similar algebraic objects: (1) the construction of infinite-dimensional algebras with striking new features; and (2) the links between group theory and holomorphic dynamics, with particular focus on higher-dimensional mappings.
DFG Programme Research Grants
 
 

Additional Information

Textvergrößerung und Kontrastanpassung