Realization of arbitrary Lie algebras by automorphisms of $\mathrm{CR}$ manifolds and symmetries of differential equations
- 作者: Stepanova M.A.1
-
隶属关系:
- Steklov Mathematical Institute of Russian Academy of Sciences
- 期: 卷 88, 编号 2 (2024)
- 页面: 127-152
- 栏目: Articles
- URL: https://bakhtiniada.ru/1607-0046/article/view/254266
- DOI: https://doi.org/10.4213/im9469
- ID: 254266
如何引用文章
开放存取
##reader.subscriptionAccessGranted##
订阅存取
详细
For any finite-dimensional real Lie algebra $\mathfrak{h}$, we constructa germ of a real analytic hypersurface in complex space such that its Lie algebraof infinitesimal holomorphic automorphisms is isomorphic to $\mathfrak{h}$.For any $\mathfrak{h}$, we also construct a system of partial differential equations whoseLie algebra of symmetries is isomorphic to the complexificationof the algebra $\mathfrak{h}$.
作者简介
Mariya Stepanova
Steklov Mathematical Institute of Russian Academy of Sciences
Scopus 作者 ID: 57197703423
Researcher ID: AAG-1157-2019
without scientific degree, no status
参考
- H. Poincare, “Les fonctions analytiques de deux variables et la representation conforme”, Rend. Circ. Mat. Palermo, 23 (1907), 185–220
- В. К. Белошапка, “Симметрии вещественных гиперповерхностей трехмерного комплексного пространства”, Матем. заметки, 78:2 (2005), 171–179
- А. Е. Туманов, Г. Б. Шабат, “Реализация линейных групп Ли билогоморфными автоморфизмами ограниченных областей”, Функц. анализ и его прил., 24:3 (1990), 94–95
- J. Winkelmann, Realizing connected Lie groups as automorphism groups of complex manifolds
- E. Cartan, “Sur la geometrie pseudo-conforme des hypersurfaces de l'espace de deux variables complexes. II”, Ann. Scuola Norm. Super. Pisa Cl. Sci. (2), 1:4 (1932), 333–354
- B. Segre, “Questioni geometriche legate colla teoria delle funzioni di due variabili complesse”, Rend. Sem. Mat. Roma (2), 7:2 (1932), 59–107
- H. Gaussier, J. Merker, “Symmetries of partial differential equations”, J. Korean Math. Soc., 40:3 (2003), 517–561
- I. Kossovskiy, R. Shafikov, “Analytic differential equations and spherical real hypersurfaces”, J. Differential Geom., 102:1 (2016), 67–126
- М. А. Степанова, “Об автоморфизмах прямого произведения CR-многообразий”, Матем. заметки, 111:2 (2022), 287–296
- M. Baouendi, P. Ebenfelt, L. P. Rothschild, “CR automorphisms of real analytic manifolds in complex space”, Comm. Anal. Geom., 6:2 (1998), 291–315
- А. Б. Сухов, “О преобразованиях аналитических CR-структур”, Изв. РАН. Сер. матем., 67:2 (2003), 101–132
- J. Grabowski, G. Marmo, A. Perelomov, A. Simoni, “Remarks on Virasoro and Kac–Moody algebras”, Internat. J. Modern Phys. A, 11:28 (1996), 4969–4984
- В. Г. Кац, Бесконечномерные алгебры Ли, Мир, М., 1993, 426 с.
补充文件
