REPRESENTASI su(2) DAN KOMPLEKSIFIKASI su(2)_C=sl(2,C) PADA RUANG VEKTOR POLINOM HOMOGEN

Authors

  • Edi Kurniadi Departemen Matematika FMIPA Unpad
  • Badrulfalah Badrulfalah Departemen Matematika FMIPA Unpad
  • Nurul Gusriani Departemen Matematika FMIPA Unpad

DOI:

https://doi.org/10.24269/silogisme.v9i2.9259

Abstract

Aljabar Lie su(N) mempunyai kompleksifikasi sl(N,C). Dengan kata lain, suNC≅sl(N,C). Dalam artikel ini, dipelajari representasi aljabar Lie su(N) dan sl(N,C) khususnya untuk N=2 yang direalisasikan pada ruang vektor polinom homogen kompleks dua variabel berderajat dua. Tujuannya adalah untuk mengkonstruksi representasi sl(2,C) dari representasi su(2) dan  membuktikan bahwa representasi yang diperoleh bersifat unitar dan tak tereduksi. Selanjutnya, karena grup Lie dari  su(2) bersifat simply connected maka representasi su(2) dapat dikonstruksi dari grup Lie-nya. Di sisi lain, karena su2C≅sl(2,C) maka representasi dari sl(2,C) dapat dikonstruksi melalui perluasan linear-kompleks dari representasi su(2) dan hasilnya dapat dinyatakan dalam bentuk operator linear.

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Published

2024-12-15

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Vol. 9 No. 2 (2024): Desember

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