On the basis of the Bruhat decomposition, the subgroups generated by pairs of unipotent short root subgroups in Chevalley groups of type B , C , and F4 over an arbitrary field are described. Moreover, the orbits of a Chevalley group acting by conjugation on such pairs are classified.

in the 1960's noboru iwahori and hideya matsumoto, eiichi abe and kazuo suzuki, and michael stein discovered that chevalley groups $g=g(phi,r)$ over a semilocal ring admit remarkable gauss decomposition $g=tuu^-u$, where $t=t(phi,r)$ is a split maximal torus, whereas $u=u(phi,r)$ and $u^-=u^-(phi,r)$ are unipotent radicals of two opposite borel subgroups $b=b(phi,r)$ and $b^-=b^-(phi,r)$ contai...

THE EXCEPTIONAL SIMPLE LIE ALGEBRAS F4 AND E6 By CLAUDE CHEVALLEY AND R. D. SCHAFER DEPARTMENTS OF MATHEMATICS, COLUMBIA UNIVERSITY AND UNIVERSITY OF PENNSYLVANIA Communicated by A. A. Albert, December 28, 1949 Let K be an algebraically closed field of characteristic 0. The exceptional simple Jordan algebra 3 over K is the (non-associative) algebra of dimension 27 whose elements are 3 X 3 Hermi...

The famous primary and cyclic decomposition theorems along with the tightly related rational and Jordan canonical forms are extended to linear spaces of infinite dimensions with counterexamples showing the scope of extensions.

the famous primary and cyclic decomposition theorems along with the tightly related rational and jordan canonical forms are extended to linear spaces of infinite dimensions with counterexamples showing the scope of extensions.