DERIVATIONS OF LOCAL k-TH HESSIAN ALGEBRAS OF SINGULARITIES

Naveed Hussain; Stephen S.T. Yau; Huaiqing Zuo

doi:10.1216/rmj.2023.53.65

DERIVATIONS OF LOCAL k-TH HESSIAN ALGEBRAS OF SINGULARITIES

Naveed Hussain
, Stephen S.T. Yau
, Huaiqing Zuo

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

1 Scopus citations

Abstract

In our previous work, we introduced a series of new derivation Lie algebras L_k(V) associated to an isolated hypersurface singularity (V, 0). These are new analytic invariants of singularities. Here, we investigate L₂(V) for fewnomial isolated singularities and obtain the formula of λ_k(V) (i.e., the dimension of L_k(V)) for trinomial singularities. Furthermore, we prove the sharp upper estimate conjecture for L₂(V). This is a continuation of our previous work (Math. Z. 298:3-4 (2021), 1813–1829). We proposed two new conjectures for τ_k(V) and λ_k(V) and we prove these conjectures for a large class of singularities.

Original language	English
Pages (from-to)	65-87
Number of pages	23
Journal	Rocky Mountain Journal of Mathematics
Volume	53
Issue number	1
DOIs	https://doi.org/10.1216/rmj.2023.53.65
State	Published - Feb 2023
Externally published	Yes

Bibliographical note

Publisher Copyright:
© Rocky Mountain Mathematics Consortium.

Keywords

Hessian algebra
derivation Lie algebra
isolated singularity

ASJC Scopus subject areas

General Mathematics

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10.1216/rmj.2023.53.65

Cite this

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title = "DERIVATIONS OF LOCAL k-TH HESSIAN ALGEBRAS OF SINGULARITIES",

abstract = "In our previous work, we introduced a series of new derivation Lie algebras Lk(V) associated to an isolated hypersurface singularity (V, 0). These are new analytic invariants of singularities. Here, we investigate L2(V) for fewnomial isolated singularities and obtain the formula of λk(V) (i.e., the dimension of Lk(V)) for trinomial singularities. Furthermore, we prove the sharp upper estimate conjecture for L2(V). This is a continuation of our previous work (Math. Z. 298:3-4 (2021), 1813–1829). We proposed two new conjectures for τk(V) and λk(V) and we prove these conjectures for a large class of singularities.",

keywords = "Hessian algebra, derivation Lie algebra, isolated singularity",

author = "Naveed Hussain and Yau, \{Stephen S.T.\} and Huaiqing Zuo",

note = "Publisher Copyright: {\textcopyright} Rocky Mountain Mathematics Consortium.",

year = "2023",

month = feb,

doi = "10.1216/rmj.2023.53.65",

language = "English",

volume = "53",

pages = "65--87",

journal = "Rocky Mountain Journal of Mathematics",

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publisher = "Rocky Mountain Mathematics Consortium",

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T1 - DERIVATIONS OF LOCAL k-TH HESSIAN ALGEBRAS OF SINGULARITIES

AU - Hussain, Naveed

AU - Yau, Stephen S.T.

AU - Zuo, Huaiqing

N1 - Publisher Copyright: © Rocky Mountain Mathematics Consortium.

PY - 2023/2

Y1 - 2023/2

N2 - In our previous work, we introduced a series of new derivation Lie algebras Lk(V) associated to an isolated hypersurface singularity (V, 0). These are new analytic invariants of singularities. Here, we investigate L2(V) for fewnomial isolated singularities and obtain the formula of λk(V) (i.e., the dimension of Lk(V)) for trinomial singularities. Furthermore, we prove the sharp upper estimate conjecture for L2(V). This is a continuation of our previous work (Math. Z. 298:3-4 (2021), 1813–1829). We proposed two new conjectures for τk(V) and λk(V) and we prove these conjectures for a large class of singularities.

AB - In our previous work, we introduced a series of new derivation Lie algebras Lk(V) associated to an isolated hypersurface singularity (V, 0). These are new analytic invariants of singularities. Here, we investigate L2(V) for fewnomial isolated singularities and obtain the formula of λk(V) (i.e., the dimension of Lk(V)) for trinomial singularities. Furthermore, we prove the sharp upper estimate conjecture for L2(V). This is a continuation of our previous work (Math. Z. 298:3-4 (2021), 1813–1829). We proposed two new conjectures for τk(V) and λk(V) and we prove these conjectures for a large class of singularities.

KW - Hessian algebra

KW - derivation Lie algebra

KW - isolated singularity

UR - https://www.scopus.com/pages/publications/85163528298

U2 - 10.1216/rmj.2023.53.65

DO - 10.1216/rmj.2023.53.65

M3 - Article

AN - SCOPUS:85163528298

SN - 0035-7596

VL - 53

SP - 65

EP - 87

JO - Rocky Mountain Journal of Mathematics

JF - Rocky Mountain Journal of Mathematics

IS - 1

ER -

DERIVATIONS OF LOCAL k-TH HESSIAN ALGEBRAS OF SINGULARITIES

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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