Basic Concept of Lie Groups

Mukesh Kumar Choudhary; Dr. S. Biswas

doi:https://doi.org/10.14445/22315373/IJMTT-V67I4P509

International Journal of Mathematics Trends and Technology

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Volume 67 | Issue 4 | Year 2021 | Article Id. IJMTT-V67I4P509 | DOI : https://doi.org/10.14445/22315373/IJMTT-V67I4P509

Basic Concept of Lie Groups

Mukesh Kumar Choudhary, Dr. S. Biswas

Abstract

Lie groups is an intersection of two fundamental fields of mathematics: algebra and geometry. Lie groups is a first of all the group and secondly it is a smooth manifold which is a specific kind of geometric objects. The circle and the sphere are example of smooth manifolds. A circle has a continuous group of symmetries. You can rotate the circle an arbitrarily small amount and it looks the same. Finally, we can say that A Lie group is a group of symmetries where the symmetries are continuous.

Keywords

History of lie group, Definition of Lie group, Classification of Lie group, Importance of Lie groups

References

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Citation :

Mukesh Kumar Choudhary, Dr. S. Biswas, "Basic Concept of Lie Groups," International Journal of Mathematics Trends and Technology (IJMTT), vol. 67, no. 4, pp. 62-66, 2021. Crossref, https://doi.org/10.14445/22315373/IJMTT-V67I4P509