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Maximal Antipodal Subgroups and Covering Homomorphisms with Odd Degree

Year 2024, , 153 - 156, 23.04.2024
https://doi.org/10.36890/iejg.1436313

Abstract

We show that all of maximal antipodal subgroups in compact Lie groups, which are not necessarily connected, do not change through covering homomorphisms with odd degree.

References

  • [1] Chen, B.-Y.: Geometry and topology of maximal antipodal sets and related topics, Rom. J. Math. Comput. Sci., 23, 6–25 (2023).
  • [2] Chen, B.-Y., Nagano, T.: A Riemannian geometric invariant and its applications to a problem of Borel and Serre. Trans. Amer. Math. Soc. 308, 273–297 (1988).
  • [3] Tanaka, M. S., Tasaki, H.: Antipodal sets of symmetric R-spaces. Osaka J. Math. 50, 161–169 (2013).
  • [4] Tanaka, M. S., Tasaki, H.: Maximal antipodal subgroups of the automorphism groups of compact Lie algebras. Springer Proceedings in Mathematics & Statistics 203, Y. J. Suh et al. (eds.), "Hermitian-Grassmannian Submanifolds", 39–47 (2017).
  • [5] Tanaka, M. S., Tasaki, H.: Maximal antipodal subgroups of some compact classical Lie groups. J. Lie Theory 27, 801–829 (2017).
  • [6] Tanaka, M. S., Tasaki, H.: Maximal antipodal sets of compact classical symmetric spaces and their cardinalities I. Differ. Geom. Appl. 73 101682 (2020).
Year 2024, , 153 - 156, 23.04.2024
https://doi.org/10.36890/iejg.1436313

Abstract

References

  • [1] Chen, B.-Y.: Geometry and topology of maximal antipodal sets and related topics, Rom. J. Math. Comput. Sci., 23, 6–25 (2023).
  • [2] Chen, B.-Y., Nagano, T.: A Riemannian geometric invariant and its applications to a problem of Borel and Serre. Trans. Amer. Math. Soc. 308, 273–297 (1988).
  • [3] Tanaka, M. S., Tasaki, H.: Antipodal sets of symmetric R-spaces. Osaka J. Math. 50, 161–169 (2013).
  • [4] Tanaka, M. S., Tasaki, H.: Maximal antipodal subgroups of the automorphism groups of compact Lie algebras. Springer Proceedings in Mathematics & Statistics 203, Y. J. Suh et al. (eds.), "Hermitian-Grassmannian Submanifolds", 39–47 (2017).
  • [5] Tanaka, M. S., Tasaki, H.: Maximal antipodal subgroups of some compact classical Lie groups. J. Lie Theory 27, 801–829 (2017).
  • [6] Tanaka, M. S., Tasaki, H.: Maximal antipodal sets of compact classical symmetric spaces and their cardinalities I. Differ. Geom. Appl. 73 101682 (2020).
There are 6 citations in total.

Details

Primary Language English
Subjects Algebraic and Differential Geometry
Journal Section Research Article
Authors

Makiko Tanaka 0000-0002-0621-4777

Hiroyuki Tasaki This is me 0000-0003-2546-0065

Early Pub Date April 6, 2024
Publication Date April 23, 2024
Submission Date February 14, 2024
Acceptance Date April 1, 2024
Published in Issue Year 2024

Cite

APA Tanaka, M., & Tasaki, H. (2024). Maximal Antipodal Subgroups and Covering Homomorphisms with Odd Degree. International Electronic Journal of Geometry, 17(1), 153-156. https://doi.org/10.36890/iejg.1436313
AMA Tanaka M, Tasaki H. Maximal Antipodal Subgroups and Covering Homomorphisms with Odd Degree. Int. Electron. J. Geom. April 2024;17(1):153-156. doi:10.36890/iejg.1436313
Chicago Tanaka, Makiko, and Hiroyuki Tasaki. “Maximal Antipodal Subgroups and Covering Homomorphisms With Odd Degree”. International Electronic Journal of Geometry 17, no. 1 (April 2024): 153-56. https://doi.org/10.36890/iejg.1436313.
EndNote Tanaka M, Tasaki H (April 1, 2024) Maximal Antipodal Subgroups and Covering Homomorphisms with Odd Degree. International Electronic Journal of Geometry 17 1 153–156.
IEEE M. Tanaka and H. Tasaki, “Maximal Antipodal Subgroups and Covering Homomorphisms with Odd Degree”, Int. Electron. J. Geom., vol. 17, no. 1, pp. 153–156, 2024, doi: 10.36890/iejg.1436313.
ISNAD Tanaka, Makiko - Tasaki, Hiroyuki. “Maximal Antipodal Subgroups and Covering Homomorphisms With Odd Degree”. International Electronic Journal of Geometry 17/1 (April 2024), 153-156. https://doi.org/10.36890/iejg.1436313.
JAMA Tanaka M, Tasaki H. Maximal Antipodal Subgroups and Covering Homomorphisms with Odd Degree. Int. Electron. J. Geom. 2024;17:153–156.
MLA Tanaka, Makiko and Hiroyuki Tasaki. “Maximal Antipodal Subgroups and Covering Homomorphisms With Odd Degree”. International Electronic Journal of Geometry, vol. 17, no. 1, 2024, pp. 153-6, doi:10.36890/iejg.1436313.
Vancouver Tanaka M, Tasaki H. Maximal Antipodal Subgroups and Covering Homomorphisms with Odd Degree. Int. Electron. J. Geom. 2024;17(1):153-6.