Root shadow spaces

We give a characterization of the root shadow spaces of buildings whose types correspond to Dynkin diagrams. The results generalize earlier geometric point-line characterizations of certain spherical buildings as well as Timmesfeld's characterization of abstract root subgroups.

[1]  E. Shult,et al.  Point-line characterizations of Lie geometries , 2002 .

[2]  Mark Ronan,et al.  Lectures on Buildings , 1989 .

[3]  H. Coxeter,et al.  The Geometric vein : the Coxeter Festschrift , 1981 .

[4]  A. Cohen,et al.  Lie algebras generated by extremal elements , 1999, math/9903077.

[5]  A. Hora,et al.  Distance-Regular Graphs , 2007 .

[6]  Francis Buekenhout.  Handbook of incidence geometry : buildings and foundations , 1995 .

[7]  Jacques Tits,et al.  A Local Approach to Buildings , 1981 .

[8]  A. Cohen.  Chapter 12 – Point-Line Spaces Related to Buildings , 1995 .

[9]  H. Cuypers.  The geometry of k-transvection groups , 2006 .

[10]  P. M. Cohn.  GROUPES ET ALGÉBRES DE LIE , 1977 .

[11]  Michael Aschbacher,et al.  Corrections to “Involutions in Chevalley groups over fields of even order” , 1976, Nagoya Mathematical Journal.

[12]  A. Premet,et al.  Simple Lie algebras of small characteristic IV.: Solvable and classical roots , 2001 .

[13]  A. Premet,et al.  Simple Lie Algebras of Small Characteristic: III. The Toral Rank 2 Case , 2001 .

[14]  Bruce N. Cooperstein,et al.  The geometry of root subgroups in exceptional groups. I. , 1979 .

[15]  A. Cohen,et al.  Root filtration spaces from Lie algebras and abstract root groups , 2006 .

[16]  A. Premet,et al.  Simple Lie Algebras of Small Characteristic: I. Sandwich Elements , 1997 .

[17]  Franz Georg Timmesfeld,et al.  Abstract Root Subgroups and Simple Groups of Lie-Type , 2001 .