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Ema Carnia
Departemen Matematika, FMIPA, 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 Agus Supriatna Ananda Ayu Permatasari Ariesandy, Sena Arjun Hasibuan Asep K. Supriatna Asep K. Supriatna Asep Kuswandi Supriatna Basuki , Basuki Basuki Dwindi Agryanti Johar Edi Kurniadi Edi Kurniadi Edi Kurniadi Edi Kurniadi Edi Kurniadi Elah Dewia Endang Rusyaman Faldiyan, Muhammad Faurani, Nuraesa Nufus Hafizhah, Nur Hasibuan, Arjun Henti Henti Henti Henti Henti, Henti Herlina Napitupulu Irawati Irawati Isah . Aisah Isah Aisah Isah Aisah Kankan Parmikanti Maryati, Ati Muhammad Deni Johansyah Muhammad Faldiyan Nuraesa Nufus Faurani Nursanti Anggriani Permatasari, Ananda Ayu Setiadji, Setiadji Sisilia Sylviani Sri Wahyuni Sukono . Supriatna, Agus Valerie ​Valerie Valerie ​Valerie Yurio Windiatmoko Yurio Windiatmoko, Yurio