On the Higher Nash Blow-Up Derivation Lie Algebras of Isolated Hypersurface Singularities-Reference-Cited by-同舟云学术

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

Published:2023-04-20 Issue:8 Volume:11 Page:1935
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Asif Muhammad¹^ORCID,Al-Kenani Ahmad N.²^ORCID,Hussain Naveed³,Binyamin Muhammad Ahsan⁴

Affiliation:

1. Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore 54000, Punjab, Pakistan

2. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia

3. Department of Mathematics and Statistics, University of Agriculture, Faisalabad 38000, Punjab, Pakistan

4. Department of Mathematics, GC University Faisalabad, Faisalabad 38000, Punjab, Pakistan

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 Lkl(V) associated to isolated hypersurface singularities defined to be the Lie algebra of derivations of the local Artinian algebra Mnl(V):=Ol/⟨F,Jn⟩, i.e., Lkl(V)=Der(Mnl(V)). In this paper, we construct a new conjecture for the complete characterization of simple hypersurface singularities using the Lie algebras Lkl(V) under certain condition and prove it true for Lkl(V) when k,l=2.

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2227-7390/11/8/1935/pdf

Reference22 articles.

1. Fifteen characterizations of rational double points and simple critical points;Durfee;Enseign. Math.,1979

2. Kac-Moody Lie algebras and the universal element for the category of nilpotent Lie algebras;Santharoubane;Math. Ann.,1983

3. Solvable Lie algebras and GCMs arising from isolated singularities;Yau;Math. Z.,1986

4. Solvability of Lie algebras arising from isolated singularities and nonisolatedness of singularities defined by sl(2, C) invariant polynomials;Yau;Amer. J. Math.,1991

5. Khimshiashvili, G. (2006). Yau algebras of fewnomial singularities. Univ. Utrecht Prepr., 1352. Available online: http://www.math.uu.nl/publications/preprints/1352.pdf.