Semigroups in semi-simple Lie groups: Flag type and estimation of cocycles
Adriano Da Silva, Luiz A.B. San Martin, Joao Victor Uzita
TL;DR
This paper explores how the flag type of a semigroup in a noncompact semisimple Lie group can be determined through cocycle bounds on the flag manifold, linking algebraic and geometric properties.
Contribution
It introduces a method to recover the flag type by analyzing the existence of lower bounds for cocycles on the maximal flag manifold.
Findings
Flag type can be recovered from cocycle bounds
Cocycle lower bounds relate to geometric control sets
New algebraic-geometric connection established
Abstract
The flag type of a semigroup S of a noncompact semisimple Lie group is an algebraic tool related to the geometry of the invariant control set determined by S on the flag manifolds of G. In the present paper we show that it is possible to recover the flag type by studying the existence of lower bounds for cocycles on the maximal flag manifold
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Taxonomy
TopicsFunctional Equations Stability Results · Geometric and Algebraic Topology