THE UNIVERSAL PROPERTY OF TENSOR PRODUCT FOR REPRESENTATIONS OF LIE GROUPS - Majeed, Taghreed Hur (MAGISTRA, 2014)
The universal property of tensor product for representations of Lie groups and Lie algebras is a supporting conjugate of tensor product, which guarantees obtaining a linear map from a bilinear map. The main aim in this study is to look for a novel action with new properties on Lie group from a Lemma of Schure, the literature are concerned with studying the action of Lie algebra of two representations, one is usual and the other is the dual, while our interest in this work is focused on some actions on Lie group. In this paper, an action of tensor product for representations of Lie groups (AC-Lie group) has been defined. Furthermore, the action of action of tensor product for representations of Lie groups by duality (AAC-Lie groups), is also been found. The theoretical justifications are developed and proved supported by some concluding remarks and illustrations. Key words: universal property, tensor product, representations of Lie groups, representations of Lie algebras