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

Naveed Hussain; Ahmad N. Al-Kenani; Muhammad Arshad; Muhammad Asif

doi:10.3390/math10152618

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

Naveed Hussain^*, Ahmad N. Al-Kenani, Muhammad Arshad, Muhammad Asif

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

Hussain, Yau, and Zuo introduced the Lie algebra (Formula presented.) from the derivation of the local algebra (Formula presented.). 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 (Formula presented.) and justify the sharp upper estimate conjecture for fewnomial isolated singularities. We also verify the inequality conjecture: (Formula presented.) for a general class of singularities. Our findings are novel and an addition to the study of Lie algebra.

Original language	English
Article number	2618
Journal	Mathematics
Volume	10
Issue number	15
DOIs	https://doi.org/10.3390/math10152618
State	Published - Aug 2022
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2022 by the authors.

Keywords

Lie algebra
fewnomial
isolated hypersurface singularity
local algebra
singularities

ASJC Scopus subject areas

Computer Science (miscellaneous)
General Mathematics
Engineering (miscellaneous)

Access to Document

10.3390/math10152618

Cite this

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title = "The Sharp Upper Estimate Conjecture for the Dimension δk(V) of New Derivation Lie Algebra",

abstract = "Hussain, Yau, and Zuo introduced the Lie algebra (Formula presented.) from the derivation of the local algebra (Formula presented.). 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 (Formula presented.) and justify the sharp upper estimate conjecture for fewnomial isolated singularities. We also verify the inequality conjecture: (Formula presented.) for a general class of singularities. Our findings are novel and an addition to the study of Lie algebra.",

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AU - Hussain, Naveed

AU - Al-Kenani, Ahmad N.

AU - Arshad, Muhammad

AU - Asif, Muhammad

PY - 2022/8

Y1 - 2022/8

N2 - Hussain, Yau, and Zuo introduced the Lie algebra (Formula presented.) from the derivation of the local algebra (Formula presented.). 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 (Formula presented.) and justify the sharp upper estimate conjecture for fewnomial isolated singularities. We also verify the inequality conjecture: (Formula presented.) for a general class of singularities. Our findings are novel and an addition to the study of Lie algebra.

AB - Hussain, Yau, and Zuo introduced the Lie algebra (Formula presented.) from the derivation of the local algebra (Formula presented.). 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 (Formula presented.) and justify the sharp upper estimate conjecture for fewnomial isolated singularities. We also verify the inequality conjecture: (Formula presented.) for a general class of singularities. Our findings are novel and an addition to the study of Lie algebra.

KW - Lie algebra

KW - fewnomial

KW - isolated hypersurface singularity

KW - local algebra

KW - singularities

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