On the discrete subgroups and homogeneous spaces of nilpotent Lie groups
Open accessAbstract
Recently A, Malcev has shown that the homogeneous space of a connected nilpotent Lie group G is the direct product of a compact space and an Euclidean-space and that the compact space of this direct decomposition is also a homogeneous space of a connected subgroup of G. Any compact homogeneous space M of a connected nilpotent Lie group is of the form where is a connected simply connected nilpotent group whose structure constants are rational numbers in a suitable coordinate system and D is a discrete subgroup of G.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
Cohomology theory of Lie groups and Lie algebras
Chevalley, C. C., & Eilenberg, S. (1948) · Transactions of the American Mathematical Society · doi:10.1090/s0002-9947-1948-0024908-8 · Cited by 782 · see citing works
Cohomology Theory in Abstract Groups. I
Eilenberg, S., & MacLane, S. (1947) · Annals of Mathematics · doi:10.2307/1969215 · Cited by 324 · see citing works
Relations Between Homology and Homotopy Groups of Spaces
Eilenberg, S., & MacLane, S. (1945) · The Annals of Mathematics · doi:10.2307/1969165 · Cited by 161 · see citing works
On Everywhere Dense Imbedding of Free Groups in Lie Groups
Kuranishi, M. (1951) · Nagoya Mathematical Journal · doi:10.1017/s0027763000010059 · Cited by 104 · see citing works
Fundamentalgruppe und zweite Bettische Gruppe
Hopf, H. (1942) · Commentarii Mathematici Helvetici · doi:10.1007/bf02565629 · Cited by 58 · see citing works
On the Topological Structure of Solvable Groups
Chevalley, C. C. (1941) · Annals of Mathematics · doi:10.2307/1969255 · Cited by 55 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Samelson, H. (1952) · Bulletin of the American Mathematical Society · doi:10.1090/s0002-9904-1952-09544-6 · Cited by 219 · see citing works
- Authors
- Matsushima, Y.
- Affiliations
- Nagoya University (JP)
- Corresponding author
- Matsushima, Yozô
- Venue
- Nagoya Mathematical Journal
- Publisher
- Cambridge University Press (CUP)
- Published
- 1951-02
- Volume
- 2
- Pages
- 95-110
- ISSN
- 0027-7630 (ISSN-L)
- 2152-6842
- OpenAlex
- W1486825256
- Semantic Scholar
- 61a4436e6d6a6fc66bfbebfed5b4676e62e7affa
- Cited by
- 48
- References
- 6
- Citations by year
- 2024: 2 · 2021: 1 · 2018: 1 · 2017: 2 · 2014: 2 · 2013: 4 · 2012: 1
- FWCI
- 1.44
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Nagoya Mathematical Journal (publishedVersion)
- Project Euclid (Cornell University) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Mathematical Physics › Advanced Algebra and Geometry
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Advanced Differential Geometry Research
- Physical Sciences › Mathematics › Algebra and Number Theory › Advanced Topics in Algebra
- Keywords
- nilpotent Lie groups, homogeneous spaces, discrete subgroups, compact homogeneous spaces, structure constants, direct product decomposition
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
