The DOI matches its Crossref record.
Differential Geometry, Lie Groups, and Symmetric Spaces
Abstract
Elementary differential geometry Lie groups and Lie algebras Structure of semisimple Lie algebras Symmetric spaces Decomposition of symmetric spaces Symmetric spaces of the noncompact type Symmetric spaces of the compact type Hermitian symmetric spaces Structure of semisimple Lie groups The classification of simple Lie algebras and of symmetric spaces Solutions to exercises Some details Bibliography List of notational conventions Symbols frequently used Index Reviews for the first edition.
Overview
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
Verification
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.
Citations
Cited by
Classification of topological quantum matter with symmetries
Chiu, C.-K., Teo, J. C. Y., Schnyder, A. P., & Ryu, S. (2016) · Reviews of Modern Physics · doi:10.1103/revmodphys.88.035005 · Cited by 2,736
Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures
Altland, A., & Zirnbauer, M. R. (1997) · Physical Review B · doi:10.1103/physrevb.55.1142 · Cited by 2,402
Group representations in probability and statistics
Diaconis, P. (1988) · doi:10.1214/lnms/1215467407 · Cited by 1,381
Quantum integrable systems related to lie algebras
Olshanetsky, M. A., & Perelomov, A. M. (1983) · Physics Reports · doi:10.1016/0370-1573(83)90018-2 · Cited by 991
Interpolation Method for Adapting Reduced-Order Models and Application to Aeroelasticity
Amsallem, D., & Farhat, C. (2008) · AIAA Journal · doi:10.2514/1.35374 · Cited by 710
Metadata
- Authors
- Helgason, S.
- Venue
- Graduate Studies in Mathematics
- Publisher
- American Mathematical Society
- Published
- 2001-06-12
- ISSN
- 1065-7339 (ISSN-L)
- OpenAlex
- W1983894121
- Cited by
- 5,433
- References
- 0
- FWCI
- 43.60
- Type
- book
- Language
- en
- Open access
- closed
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
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Differential Geometry, Lie Groups, and Symmetric Spaces. https://app.cochat.ai/papers/10.1090/gsm/034
- The paper
- Helgason, S. (2001). Differential Geometry, Lie Groups, and Symmetric Spaces. Graduate Studies in Mathematics. https://doi.org/10.1090/gsm/034
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
