Linear algebraic groups in infinite dimensions

Structure Groups and Holonomy in Infinite Dimensions

We give a theorem of reduction of the structure group of a principal bundle P with regular structure group G. Then, when G is in the classes of regular Lie groups defined by T.Robart in [13], we define the closed holonomy group of a connection as the minimal closed Lie subgroup of G for which the previous theorem of reduction can be applied. We also prove an infinite dimensional version of the ...

Linear Algebraic Groups

Linear Algebraic Groups

Linear Algebraic Groups

We give a summary, without proofs, of basic properties of linear algebraic groups, with particular emphasis on reductive algebraic groups.

Linear Algebraic Groups

These are the exercises (with solutions) and the exam for the course Algebra II, winter term 2014/2015 at Bonn. Students were not assumed to have heard algebraic geometry before, just algebra. In particular, basic affine and projective geometry were introduced from scratch. The course covered the standard material up to the structure results about maximal tori and Borel subgroups. Root systems ...