PROPER AFFINE ACTIONS ON SEMISIMPLE LIE ALGEBRAS

被引：9

作者：

Smilga, Ilia ^{[1
]}

机构：

[1] Yale Univ, Dept Math, POB 208283, New Haven, CT 06520 USA

来源：

ANNALES DE L INSTITUT FOURIER | 2016年 / 66卷 / 02期

关键词：

Discrete subgroups of Lie groups; Affine groups; Auslander conjecture; Milnor conjecture; Flat affine manifolds; Adjoint representation; Margulis invariant; Quasi translation; Fee group; Schottky group; MARGULIS SPACE-TIMES; DISCONTINUOUS GROUPS; TRANSFORMATIONS;

D O I：

10.5802/aif.3026

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For any noncompact semisimple real Lie group G, we construct a group of affine transformations of its Lie algebra g whose linear part is Zariskidense in Ad G and which is free, nonabelian and acts properly discontinuously on g.

引用

页码：785 / 831

页数：47

共 50 条

[1] On the Quantum KPRV Determinants for Semisimple and Affine Lie Algebras
Anthony Joseph
Dragana Todorić
[J]. Algebras and Representation Theory, 2002, 5 : 57 - 99
[2] On the quantum KPRV determinants for semisimple and affine Lie algebras
Joseph, A
Todoric, D
[J]. ALGEBRAS AND REPRESENTATION THEORY, 2002, 5 (01) : 57 - 99
[3] TRANSITIVE ACTIONS OF SEMISIMPLE LIE ROUPS ON SPLITTED AFFINE SPACES
KHOSROVYAN, OM
[J]. IZVESTIYA VYSSHIKH UCHEBNYKH ZAVEDENII MATEMATIKA, 1987, (06): : 65 - 72
[4] SEMISIMPLE RESOLUTION OF SEMISIMPLE LIE ALGEBRAS
ONISHCHIK, AL
[J]. DOKLADY AKADEMII NAUK SSSR, 1963, 149 (05): : 1033 - &
[5] Cohomology of divergence forms and proper actions of Lie algebras
Abouqateb, Abdelhak
[J]. JOURNAL OF LIE THEORY, 2007, 17 (02) : 317 - 335
[6] SEMISIMPLE CYCLIC ELEMENTS IN SEMISIMPLE LIE ALGEBRAS
Elashvili, A. G.
Jibladze, M.
Kac, V. G.
[J]. TRANSFORMATION GROUPS, 2022, 27 (02) : 429 - 470
[7] Constructing semisimple subalgebras of semisimple Lie algebras
de Graaf, Willem A.
[J]. JOURNAL OF ALGEBRA, 2011, 325 (01) : 416 - 430
[8] SEMISIMPLE CYCLIC ELEMENTS IN SEMISIMPLE LIE ALGEBRAS
A. G. ELASHVILI
M. JIBLADZE
V. G. KAC
[J]. Transformation Groups, 2022, 27 : 429 - 470
[9] Projections of Semisimple Lie Algebras
Gein, A. G.
[J]. ALGEBRA AND LOGIC, 2019, 58 (02) : 103 - 114
[10] Projections of Semisimple Lie Algebras
A. G. Gein
[J]. Algebra and Logic, 2019, 58 : 103 - 114

← 1 2 3 4 5 →