A NOTE ON ENDOMORPHISMS OF MODULES OVER
REDUCTIVE LIE GROUPS AND ALGEBRAS

Andreas \v{C}ap

Key words: Reductive Lie group, reductive Lie algebra,
reducible representation.

1991 Math. Subject Classification: 17B10, 22E46.

Abstract: We show how to apply the basic ideas of linear
algebra to endomorphisms of modules over reductive Lie groups and
algebras, thus obtaining notions of determinant, trace and more
generally characteristic coefficients of such endomorphisms which are
adapted to the situation. Finally, we show how these ideas can be
applied to study locally trivial bundles of such modules over smooth
manifolds.