Mustansiriyah Journal of Pure and Applied Sciences

The ACTION OF HOM SPACE AND TENSOR PRODUCT OF LIE ALGEBRAS

Shahad Hashim

University Tikrit

Taghreed Majeed

DOI: https://doi.org/10.47831/mjpas.v3i3.258

Keywords: Hom-space, Tensor product , Direct sum , Dual of representation of Lie algebras, Action of Lie Algebra

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Abstract

The primary goal of this study is to explore the Triple Action of Representation Lie Algebras (ATHS) with unique characteristics on Lie algebra using Schur's lemma , which states that the action of the tensor product of Lie algebras representation has interesting property. This involves examining the interaction of Lie algebra representations, focusing on specific actions within Lie algebras. A new approach to the tensor product and direct sum for Lie algebra representations has been introduced. Additionally, the study explores the relationship between the actions of Hom space and tensor product. The main goal is to achieve results on Lie algebra representations by utilizing a new structure comprising six representations and their corresponding actions.