Classifying spaces for commutativity of low-dimensional Lie groups

被引：5

作者：

Antolin-Camarena, Omar ^{[1
]}

Gritschacher, Simon Philipp ^{[2
]}

Villarreal, Bernardo ^{[1
]}

机构：

[1] Univ Nacl Autonoma Mexico, Inst Matemat, Mexico City, DF, Mexico

[2] Univ Copenhagen, Ctr Symmetry & Deformat, Copenhagen, Denmark

来源：

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY | 2020年 / 169卷 / 03期

基金：

新加坡国家研究基金会;

关键词：

COMMUTING ELEMENTS; TUPLES;

D O I：

10.1017/S0305004119000240

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For each of the groups G = O(2), SU(2), U(2), we compute the integral and -cohomology rings of B(com)G (the classifying space for commutativity of G), the action of the Steenrod algebra on the mod 2 cohomology, the homotopy type of E(com)G (the homotopy fiber of the inclusion B(com)G -> BG), and some low-dimensional homotopy groups of B(com)G.

引用

页码：433 / 478

页数：46

共 50 条

[1] A classifying space for commutativity in Lie groups
Adem, Alejandro
Manuel Gomez, Jose
[J]. ALGEBRAIC AND GEOMETRIC TOPOLOGY, 2015, 15 (01): : 493 - 535
[2] Moduli spaces of low-dimensional Lie superalgebras
Fialowski, Alice
Penkava, Michael
[J]. INTERNATIONAL JOURNAL OF MATHEMATICS, 2021, 32 (09)
[3] On the second homotopy group of the classifying space for commutativity in Lie groups
Bernardo Villarreal
[J]. Geometriae Dedicata, 2023, 217
[4] ON SPACES WITH VANISHING LOW-DIMENSIONAL HOMOTOPY GROUPS
WHITEHEAD, GW
[J]. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1948, 34 (05) : 207 - 211
[5] RELATIONS AMONG LOW-DIMENSIONAL SIMPLE LIE GROUPS
Gilmore, Robert
[J]. JOURNAL OF GEOMETRY AND SYMMETRY IN PHYSICS, 2012, 28 : 1 - 45
[6] On the second homotopy group of the classifying space for commutativity in Lie groups
Villarreal, Bernardo
[J]. GEOMETRIAE DEDICATA, 2023, 217 (03)
[7] A Note about Integrable Systems on Low-dimensional Lie Groups and Lie Algebras
Alexey Bolsinov
Jinrong Bao
[J]. Regular and Chaotic Dynamics, 2019, 24 : 266 - 280
[8] A Note about Integrable Systems on Low-dimensional Lie Groups and Lie Algebras
Bolsinov, Alexey
Bao, Jinrong
[J]. REGULAR & CHAOTIC DYNAMICS, 2019, 24 (03): : 266 - 280
[9] Complex, symplectic, and contact structures on low-dimensional lie groups
Smolentsev N.K.
[J]. Journal of Mathematical Sciences, 2015, 207 (4) : 551 - 613
[10] LOW-DIMENSIONAL COHOMOLOGY GROUPS OF THE LIE ALGEBRAS W(a, b)
Gao, Shoulan
Jiang, Cuipo
Pei, Yufeng
[J]. COMMUNICATIONS IN ALGEBRA, 2011, 39 (02) : 397 - 423

← 1 2 3 4 5 →