EXISTENCE OF HOLOMORPHIC FUNCTIONS ON NILPOTENT LIE GROUPS

被引：0

作者：

Mushkarov, Oleg ^{[1
]}

Yankov, Christian ^{[2
]}

机构：

[1] Bulgarian Acad Sci, Inst Math & Informat, BU-1113 Sofia, Bulgaria

[2] Eastern Connecticut State Univ, Dept Math & Comp Sci, Willimantic, CT 06226 USA

来源：

COMPTES RENDUS DE L ACADEMIE BULGARE DES SCIENCES | 2014年 / 67卷 / 09期

关键词：

almost complex manifolds; holomorphic functions; nilpotent Lie groups; SYMPLECTIC-MANIFOLDS; ALGEBRAS;

D O I：

暂无

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

We classify real 4 and 6-dimensional nilpotent Lie algebras for which every left-invariant almost complex structure on the corresponding Lie group has non-constant local holomorphic functions. We also obtain a simple algebraic characterization of 2-step nilpotent Lie algebras with the same property.

引用

页码：1187 / 1192

页数：6

共 50 条

[1] HOLOMORPHIC REPRESENTATIONS OF NILPOTENT LIE GROUPS
GOODMAN, R
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1979, 31 (01) : 115 - 137
[2] Holomorphic functions of a basis of a nilpotent Lie algebra
Dosiev, AA
[J]. FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, 2000, 34 (04) : 302 - 304
[3] Holomorphic Functions of a Basis of a Nilpotent Lie Algebra
A. A. Dosiev
[J]. Functional Analysis and Its Applications, 2000, 34 : 302 - 304
[4] The existence of soliton metrics for nilpotent Lie groups
Payne, Tracy L.
[J]. GEOMETRIAE DEDICATA, 2010, 145 (01) : 71 - 88
[5] Existence of isometric immersions into nilpotent Lie groups
Jorge H. S. de Lira
Marcos F. de Melo
[J]. Geometriae Dedicata, 2012, 157 : 339 - 365
[6] Existence of isometric immersions into nilpotent Lie groups
de Lira, Jorge H. S.
de Melo, Marcos F.
[J]. GEOMETRIAE DEDICATA, 2012, 157 (01) : 339 - 365
[7] The existence of soliton metrics for nilpotent Lie groups
Tracy L. Payne
[J]. Geometriae Dedicata, 2010, 145 : 71 - 88
[8] INVARIANT HOLOMORPHIC FUNCTIONS ON REDUCTIVE LIE GROUPS
BARTH, W
OTTE, M
[J]. MATHEMATISCHE ANNALEN, 1973, 201 (02) : 97 - 112
[9] On the existence of nilsolitons on 2-step nilpotent Lie groups
Oscari, David
[J]. ADVANCES IN GEOMETRY, 2014, 14 (03) : 483 - 497
[10] On Holomorphic Realizations of Nilpotent Lie Algebras
Akopyan, R. S.
Loboda, A. V.
[J]. FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, 2019, 53 (02) : 124 - 128

← 1 2 3 4 5 →