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Herlina Napitupulu
Departemen Matematika, Fakultas Matematika Dan Ilmu Pengetahuan Alam, Universitas Padjadjaran
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Journal : ComTech: Computer, Mathematics and Engineering Applications

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The Existence of Affine Structures on the Borel Subalgebra of Dimension 6 Edi Kurniadi; Ema Carnia; Herlina Napitupulu
ComTech: Computer, Mathematics and Engineering Applications Vol. 12 No. 1 (2021): ComTech
Publisher : Bina Nusantara University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21512/comtech.v12i1.6581

Abstract

The notion of affine structures arises in many fields of mathematics, including convex homogeneous cones, vertex algebras, and affine manifolds. On the other hand, it is well known that Frobenius Lie algebras correspond to the research of homogeneous domains. Moreover, there are 16 isomorphism classes of 6-dimensional Frobenius Lie algebras over an algebraically closed field. The research studied the affine structures for the 6-dimensional Borel subalgebra of a simple Lie algebra. The Borel subalgebra was isomorphic to the first class of Csikós and Verhóczki’s classification of the Frobenius Lie algebras of dimension 6 over an algebraically closed field. The main purpose was to prove that the Borel subalgebra of dimension 6 was equipped with incomplete affine structures. To achieve the purpose, the axiomatic method was considered by studying some important notions corresponding to affine structures and their completeness, Borel subalgebras, and Frobenius Lie algebras. A chosen Frobenius functional of the Borel subalgebra helped to determine the affine structure formulas well. The result shows that the Borel subalgebra of dimension 6 has affine structures which are not complete. Furthermore, the research also gives explicit formulas of affine structures. For future research, another isomorphism class of 6-dimensional Frobenius Lie algebra still needs to be investigated whether it has complete affine structures or not.
Co-Authors Adi Suripto, Adi Agus Santoso Aisyah, Ranti Rivani Akmal, Muhammad Novrizal Albert Raja Harungguan Alit Kartiwa Alit Kartiwa Ariesandy, Sena Asep K. Supriatna Asep K. Supriatna Asep Kuswandi Supriatna Balqis, Viona Prisyella Betty Subartini Darmawan, Muhammad Rizky Diah Chaerani Dwi Purnomo Dwi Susanti Dwi Susanti Edi Kurniadi Edi Kurniadi Edi Kurniadi Ema Carnia Eman Lesmana Erwin Harahap Ewen Hokijuliandy Fasa, Rayyan Al Muddatstsir Fauziyah, Wida Nurul Febrianty, Popy Firdaniza Firdaniza Firdaus, Hamidah 'Alina Firosi, Valeska Isma Ghazali, Puspa Liza Hadiana, Asep Id Helma Syifa Izzadiana Hidayana, Rizki Apriva Ida Widianingsih Ira Sumiati Ismail Bin Mohd Jeane R. M. D. P Chantique Julita Nahar, Julita Melina Melina Michael Lim Michelle Selina Buntara Muhammad Arief Budiman Muhammad Deni Johansyah Muhammad Helambang Prakasa Yudha Muhammad Ribhan Hadiyan Nabilla, Ulya Norizan Mohamed Novitasari, Ela Nurkasyifah, Fathimah Syifa Nursanti Anggriani Nurul Gusriani Nurul Gusriani, Nurul Rahmadini, Nurhaliza Riaman Riaman Ridwan Pandiya Salsabila, Thania Nur Saprilian Hidayat Saputra, Jumadil Satyaputra, Ida Bagus Wira Krishna Siti Aizal Yasni Ellena Sudrajat Supian Suhaimi, Nurnisaa binti Abdullah Sukono Sukono Supian, Sudradjat Supian, Sudrajat Sutisna, Sarah Syahla, Raynita Valentina Adimurti Kusumaningtyas Valerie ​Valerie Valerie ​Valerie Viona Prisyella Balqis Wida Nurul Fauziyah Yosza Dasril Yudha, Muhammad Helambang Prakasa Yulison Herry Chrisnanto Yuyun Hidayat