THE LIE ALGEBRA su(3) REPRESENTATION WITH RESPECT TO ITS BASIS

Authors

  • Edi Kurniadi Departemen Matematika FMIPA Unpad
  • Kankan Parmikanti Departemen Matematika FMIPA Unpad

DOI:

https://doi.org/10.25077/jmua.13.3.163-169.2024

Keywords:

Anti-Hermitian Matrices, Derived Representation, $\mathrm{SU}(3)$, $\mathfrak{su}(3)$

Abstract

The eight-dimensional Lie algebra of 3×3 anti-Hermitian matrices with
its traces equal to zero is denoted by su(3) whose Lie group is denoted by SU(3). The
research aims to provide all representations of su(3) with respect to its basis which is
realized on the three complex variables homogeneous polynomials P1 of degree three. The first step is to construct representations of SU(3) on the space H and the second step is to find all derived representations of SU(3). The obtained results are eight explicit formulas of representations su(3) ↷ P1.

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Author Biographies

Edi Kurniadi, Departemen Matematika FMIPA Unpad

Edi Kurniadi adalah Associate Professor sekaligus peneliti di Departemen Matematika FMIPA Unpad dengan fokus kajiannya adalah teori representasi grup dan Aljabar Lie. Gelar Ph.D diperoleh dari Graduate School of Mathematics Nagoya University, Jepang pada tahun 2019.

Kankan Parmikanti, Departemen Matematika FMIPA Unpad

Kankan Parmikanti adalah dosen senior di Departemen Matematika Unpad dengan bidang kajian Matematika Terapan: Pemodelan Stokastik. Mata Kuliah yang diampu selain kalkulus adalah mata kuliah matematika diskrit.

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Published

31-07-2024

How to Cite

Kurniadi, E., & Parmikanti, K. (2024). THE LIE ALGEBRA su(3) REPRESENTATION WITH RESPECT TO ITS BASIS. Jurnal Matematika UNAND, 13(3), 163–169. https://doi.org/10.25077/jmua.13.3.163-169.2024

Issue

Vol. 13 No. 3 (2024)

Section

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