Orthogonal decompositions of Lie algebras over finite commutative rings

Journal article

Authors/Editors

SONGPON SRIWONGSA

Strategic Research Themes

Digital Transformation (Strategic Research Themes)

Publication Details

Author list: Songpon Sriwongsa

Publisher: World Scientific Publishing

Publication year: 2021

Journal: Journal of Algebra and Its Applications (0219-4988)

Volume number: 21

Issue number: 12

ISSN: 0219-4988

eISSN: 1793-6829

URL: https://www.worldscientific.com/doi/10.1142/S0219498823500068

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Abstract

Let R be a finite commutative ring with identity. In this paper, we give a necessary
condition for the existence of an orthogonal decomposition of the special linear Lie
algebra over R. Additionally, we study orthogonal decompositions of the symplectic Lie
algebra and the special orthogonal Lie algebra over R.

Keywords

Cartan subalgebras, local rings, orthogonal decomposition