On the Higher Nash Blow-Up Derivation Lie Algebras of Isolated Hypersurface Singularities

Muhammad Asif; Ahmad N. Al-Kenani; Naveed Hussain; Muhammad Ahsan Binyamin

doi:10.3390/math11081935

On the Higher Nash Blow-Up Derivation Lie Algebras of Isolated Hypersurface Singularities

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

^*Corresponding author for this work

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

Abstract

It is a natural question to ask whether there is any Lie algebra that completely characterize simple singularities? The higher Nash blow-up derivation Lie algebras (Formula presented.) associated to isolated hypersurface singularities defined to be the Lie algebra of derivations of the local Artinian algebra (Formula presented.), i.e., (Formula presented.). In this paper, we construct a new conjecture for the complete characterization of simple hypersurface singularities using the Lie algebras (Formula presented.) under certain condition and prove it true for (Formula presented.) when (Formula presented.).

Original language	English
Article number	1935
Journal	Mathematics
Volume	11
Issue number	8
DOIs	https://doi.org/10.3390/math11081935
State	Published - Apr 2023
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2023 by the authors.

Keywords

Cartan matrix
Jacobian matrix
higher Nash blow-up
isolated singularity

ASJC Scopus subject areas

Computer Science (miscellaneous)
General Mathematics
Engineering (miscellaneous)

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10.3390/math11081935

Cite this

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title = "On the Higher Nash Blow-Up Derivation Lie Algebras of Isolated Hypersurface Singularities",

abstract = "It is a natural question to ask whether there is any Lie algebra that completely characterize simple singularities? The higher Nash blow-up derivation Lie algebras (Formula presented.) associated to isolated hypersurface singularities defined to be the Lie algebra of derivations of the local Artinian algebra (Formula presented.), i.e., (Formula presented.). In this paper, we construct a new conjecture for the complete characterization of simple hypersurface singularities using the Lie algebras (Formula presented.) under certain condition and prove it true for (Formula presented.) when (Formula presented.).",

keywords = "Cartan matrix, Jacobian matrix, higher Nash blow-up, isolated singularity",

author = "Muhammad Asif and Al-Kenani, \{Ahmad N.\} and Naveed Hussain and Binyamin, \{Muhammad Ahsan\}",

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doi = "10.3390/math11081935",

language = "English",

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T1 - On the Higher Nash Blow-Up Derivation Lie Algebras of Isolated Hypersurface Singularities

AU - Asif, Muhammad

AU - Al-Kenani, Ahmad N.

AU - Hussain, Naveed

AU - Binyamin, Muhammad Ahsan

PY - 2023/4

Y1 - 2023/4

N2 - It is a natural question to ask whether there is any Lie algebra that completely characterize simple singularities? The higher Nash blow-up derivation Lie algebras (Formula presented.) associated to isolated hypersurface singularities defined to be the Lie algebra of derivations of the local Artinian algebra (Formula presented.), i.e., (Formula presented.). In this paper, we construct a new conjecture for the complete characterization of simple hypersurface singularities using the Lie algebras (Formula presented.) under certain condition and prove it true for (Formula presented.) when (Formula presented.).

AB - It is a natural question to ask whether there is any Lie algebra that completely characterize simple singularities? The higher Nash blow-up derivation Lie algebras (Formula presented.) associated to isolated hypersurface singularities defined to be the Lie algebra of derivations of the local Artinian algebra (Formula presented.), i.e., (Formula presented.). In this paper, we construct a new conjecture for the complete characterization of simple hypersurface singularities using the Lie algebras (Formula presented.) under certain condition and prove it true for (Formula presented.) when (Formula presented.).

KW - Cartan matrix

KW - Jacobian matrix

KW - higher Nash blow-up

KW - isolated singularity

UR - https://www.scopus.com/pages/publications/85153716514

U2 - 10.3390/math11081935

DO - 10.3390/math11081935

M3 - Article

AN - SCOPUS:85153716514

SN - 2227-7390

VL - 11

JO - Mathematics

JF - Mathematics

IS - 8

M1 - 1935

ER -

On the Higher Nash Blow-Up Derivation Lie Algebras of Isolated Hypersurface Singularities

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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Cite this