Certain Types of Reductive Lie Group Action

The main aim in this book is to look for TCOA(triple co- action of reductive Lie group)with new properties on Lie group from a lemma of Schurethe literature are concerned with studying the action of Lie algebra of two representationsone is usuall and the other is dualwhile our interest in this work is focused on some action on Lie group.A new action of tensor product and direct sum for representations of Lie groups has been defind.The theoretical justifications are developed and proved supported by some concluding remarks and illustrations.