The Sharp Upper Estimate Conjecture for the Dimension δ k ( V ) of New Derivation Lie Algebra

Naveed Hussain, Ahmad N. Al-Kenani, Muhammad Arshad and Muhammad Asif
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Naveed Hussain: Department of Mathematics and Statistics, University of Agriculture, Faisalabad 38000, Pakistan
Ahmad N. Al-Kenani: Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Muhammad Arshad: Department of Mathematics and Statistics, University of Agriculture, Faisalabad 38000, Pakistan
Muhammad Asif: Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore 54000, Pakistan

Mathematics, 2022, vol. 10, issue 15, 1-12

Abstract: Hussain, Yau, and Zuo introduced the Lie algebra L k ( V ) from the derivation of the local algebra M k ( V ) : = O n / ( g + J 1 ( g ) + ⋯ + J k ( g ) ) . To find the dimension of a newly defined algebra is an important task in order to study its properties. In this regard, we compute the dimension of Lie algebra L 5 ( V ) and justify the sharp upper estimate conjecture for fewnomial isolated singularities. We also verify the inequality conjecture: δ 5 ( V ) < δ 4 ( V ) for a general class of singularities. Our findings are novel and an addition to the study of Lie algebra.

Keywords: singularities; isolated hypersurface singularity; Lie algebra; local algebra; fewnomial (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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