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

Author

Listed:
  • Naveed Hussain

    (Department of Mathematics and Statistics, University of Agriculture, Faisalabad 38000, Pakistan
    These authors contributed equally to this work.)

  • Ahmad N. Al-Kenani

    (Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
    These authors contributed equally to this work.)

  • Muhammad Arshad

    (Department of Mathematics and Statistics, University of Agriculture, Faisalabad 38000, Pakistan
    These authors contributed equally to this work.)

  • Muhammad Asif

    (Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore 54000, Pakistan
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Naveed Hussain & Ahmad N. Al-Kenani & Muhammad Arshad & Muhammad Asif, 2022. "The Sharp Upper Estimate Conjecture for the Dimension δ k ( V ) of New Derivation Lie Algebra," Mathematics, MDPI, vol. 10(15), pages 1-12, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2618-:d:872673
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    References listed on IDEAS

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    1. Naveed Hussain & Stephen S.-T. Yau & Huaiqing Zuo, 2021. "On the Dimension of a New Class of Derivation Lie Algebras Associated to Singularities," Mathematics, MDPI, vol. 9(14), pages 1-15, July.
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