Groups of finite Morley rank with a pseudoreflection action
Copyright policy )Groups of finite Morley rank with a pseudoreflection action
In this work, we give two characterisations of the general linear group as a group $G$ of finite Morley rank acting on an abelian connected group $V$ of finite Morley rank definably, faithfully and irreducibly. To be more precise, we prove that if the pseudoreflection rank of $G$ is equal to the Morley rank of $V$, then $V$ has a vector space structure over an algebraically closed field, $G\cong GL(V)$ and the action is the natural action. The same result holds also under the assumption of Prufer 2-rank of $G$ being equal to the Morley rank of $V$.
- University of Manchester United Kingdom
- University of Manchester United Kingdom
- University of Manchester United Kingdom
- University of Manchester United Kingdom
- School of Mathematics, University of Manchester United Kingdom
Representation theory for linear algebraic groups, Algebra and Number Theory, Group of finite Morley rank, groups of finite Morley rank, Groups of finite Morley rank, representations, Model-theoretic algebra, general linear groups over algebraically closed fields, 20G99, 03C60, pseudoreflection ranks, Group Theory (math.GR), Cherlin-Zilber conjecture, Pseudoreflection, Linear algebraic groups over arbitrary fields, natural action, FOS: Mathematics, pseudoreflections, Mathematics - Group Theory
Representation theory for linear algebraic groups, Algebra and Number Theory, Group of finite Morley rank, groups of finite Morley rank, Groups of finite Morley rank, representations, Model-theoretic algebra, general linear groups over algebraically closed fields, 20G99, 03C60, pseudoreflection ranks, Group Theory (math.GR), Cherlin-Zilber conjecture, Pseudoreflection, Linear algebraic groups over arbitrary fields, natural action, FOS: Mathematics, pseudoreflections, Mathematics - Group Theory
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).4 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!