The Equivalence Between (QTA) of Lie Groups and Hom- Space with Tencer Product

Authors

  • Zinah Makki Kadhim
  • Taghreed Hur Majeed

Abstract

Abstract:
The primary purpose of this research is to work out a new action of Lie group through dual representation. In our paper we mention the basic definitions, we'll discuss the study of activity for Lie group upon Hom-space utilizing equivalence relationship between tensor product and Hom. Their measures will be studied on a structure consisting of four and five vector spaces. In the end we obtain new generalizations using action of dual representation for Lie group Ǥ.

References

-B.C.Hall, "Lie Groups, lie Algebras and Representation, An Elementary .1 Introduction", Spring, USA, May, 2004.

-B. Jubin, A. Kotov, N. Poncin and V. Salnikov, Differential Graded Lie Groups .2 and Their Differential Graded Lie Algebra (Springer Undergraduate Mathematics Series, Ukraine, 2022), pp. 27-39.

-H.I. Lefta and T.H Majeed, Action of Reductive lie Groups on Hom-space and .3 Tensor product of five Representation (College of Science for Women, Baghdad- Iraq,2016), pp.325-348.

-J .Jiang, Y. Sherg and C.Zhu, Cohomologics of Relative Rota-Baxter Operators .4 on Lie Groups and Lie Algebras (arxiv e-prints, arxiv- 2018, United States of America, 2021), pp. 302-315.

-L. Cagliero and I.G. Riveta, Tensor Product and Interwining Operators Universal .5 Representation s of The Lie Algebras (arxiv prepint arxiv, United States of

America, 2022), pp.2201-10605.

- Rossmann, W., "Lie Groups; An Introduction Thraugh Linear Groups" .6 University of Ottawa, August, 24, 2006.

- T.H. Majeed "Asction of Topological Groupoid on Topological Space" The .7 International Journal of Non Linear Analysis and Applications, vol.13, No.1, pp.85- 89, 2022.

- T.T. Nguyen and V.A. Le, Representation of Real Solvable lie Algebras having .8 2- Dimensional Derived Ideal and Geometry of Coadjaint Orbits of Corresponding Lie Groups (Asian-European Journal of Mathematics, Singapore, 2022), pp. 193- 225.

- X.Zhu, C. Xu and D. Tao, Commutative Lie Group VAE for Disentanglement .9 Learning (International Conference On Machine Learning, Japan, 2021), pp. 12924- 12934.

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Published

2023-12-03