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

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

Mathematics, 2023, vol. 11, issue 8, 1-15

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

Keywords: higher Nash blow-up; Jacobian matrix; Cartan matrix; isolated singularity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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