On derivation Lie algebras of isolated complete intersection singularities

Letters in Mathematical Physics - Tập 113 - Trang 1-34 - 2023
Naveed Hussain1, Stephen S.-T. Yau2,3, Huaiqing Zuo2
1Department of Mathematics and Statistics, University of Agriculture, Faisalabad, Faisalabad, Pakistan
2Department of Mathematical Sciences, Tsinghua University, Beijing, People’s Republic of China
3Yanqi Lake Beijing Institute of Mathematical Sciences and Applications, Huairou, People’s Republic of China

Tóm tắt

In this paper, we introduce a new invariant to isolated complete intersection singularities. We use this new invariant to obtain two characterization theorems for contact simple complete intersection singularities.

Tài liệu tham khảo

Benson, M., Yau, S.S.-T.: Lie algebra and their representations arising from isolated singularities: computer method in calculating the Lie algebras and their cohomology. In: Complex Analytic Singularities. Advance Studies in Pure Mathematics 8, pp. 3–58 (1986) Brieskorn, E.: Singular elements of semi-simple algebraic groups. Actes Congres Int. Math. 2, 279–284 (1970) Chen, B., Hussain, N., Yau, S.S.-T., Zuo, H.: Variation of complex structures and variation of Lie algebras II: new Lie algebras arising from singularities. J. Differ. Geom. 115(3), 437–473 (2020) Chen, B., Xie, D., Yau, S.-T., Yau, S.S.-T., Zuo, H.: 4d N=2 SCFT and singularity theory Part II: complete intersection. Adv. Theor. Math. Phys. 21(1), 121–145 (2017) Elashvili, A., Khimshiashvili, G.: Lie algebras of simple hypersurface singularities. J. Lie Theory 16(4), 621–649 (2006) Giusti, M.: Classification des Singularitiés isolées d’intersectios compleètes simples. C. R. Acad. Sci. Paries Séér. A B 284(3), A167–A170 (1977) Hu, C., Yau, S.S.-T., Zuo, H.: Torelli Theorem for k-th Yau Algebras Over Simple Elliptic Singularities, pp. 48. preprint Hussain, N., Yau, S.S.-T., Zuo, H.: On the new \(k\)-th Yau algebras of isolated hypersurface singularities. Math. Z. 294(1–2), 331–358 (2020) Hussain, N., Yau, S.S.-T., Zuo, H.: Generalized Cartan matrices arising from new derivation Lie algebras of isolated hypersurface singularities. Pac. J. Math. 305(1), 189–217 (2020) Hussain, N., Yau, S.S.-T., Zuo, H.: Inequality conjectures on derivations of local \(k\)-th Hessain algebras associated to isolated hypersurface singularities. Math. Z. 298, 1813–1829 (2021) Hussain, N., Yau, S.S.-T., Zuo, H.: \(k\)-th Yau number of isolated hypersurface singularities and an inequality conjecture. J. Aust. Math. Soc. 110, 94–118 (2021) Hussain, N., Yau, S.S.-T., Zuo, H.: Three Types of Derivation Lie Algebras of Isolated Hypersurface Singularities, pp. 20. submitted Ma, G., Yau, S.S.-T., Zuo, H.: A Class of New \(k\)-th Local Algebras of Singularities and Its Derivation Lie Algebras, pp. 16, preprint Mather, J., Yau, S.S.-T.: Classification of isolated hypersurface singularities by their moduli algebras. Invent. Math. 69, 243–251 (1982) Santharoubane, L.J.: Kac–Moody Lie algebras and the universal element for the category of nilpotent Lie algebras. Math. Ann. 263(3), 365–370 (1983) Seiberg, N., Witten, E.: Electric–magnetic duality, monopole condensation, and confinement in \(N=2\) supersymmetric Yang–Mills theory. Nucl. Phys. B 426(1), 19–52 (1994) Seiberg, N., Witten, E.: Monopoles, duality and chiral symmetry breaking in \(N=2\) supersymmetric \(Q C D\). Nucl. Phys. B 431(3), 484–550 (1994) Wall, C.T.C.: Finite determinacy of smooth map-germs. Bull. Lond. Math. Soc. 13, 481–539 (1981) Wall, C.T.C.: Classification of unimodal isolated singularities of complete intersections. In: Orlik, P. (ed.) proceedings of Symposia in Pure Mathematics, 40ii (Singularities), pp. 625–640. American Mathematical Society (1983) Yau, S.S.-T.: Continuous family of finite-dimensional representations of a solvable Lie algebra arising from singularities. Proc. Natl. Acad. Sci. U.S.A. 80, 7694–7696 (1983) Yau, S.S.-T.: Solvable Lie algebras and generalized Cartan matrices arising from isolated singularities. Math. Z. 191, 489–506 (1986)