Let A be an involution ring, e1 , . . . , en be a full system of Hermitian idempotents in A, let every ei generate A as a two-sided ideal, and 2 ∈ A∗. In this paper, the normalizers of the groups Ep(2,A) · E(2,A, I) are calculated under natural assumptions on A, where Ep(2,A) denotes the elementary symplectic group, E(2,A, I) stands for the elementary subgroup of level I.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. Bak and Tang Guoping, “Stability for Hermitian K 1, ” J. Pure Appl. Algebra, 150, 107–121 (2000).
V. A. Petrov, “Overgroups of unitary groups,” K-Theory, 29, 147–174 (2003).
N. A. Vavilov and V. A. Petrov, “Overgroups of elementary symplectic groups,” Algebra Analiz, 15, No. 4, 72–114 (2003); English transl., St. Petersburg Math. J., 15:4, 515–543 (2004).
N. A. Vavilov and A. V. Stepanov, “Linear groups over general rings. I. Generalities,” Zap. Nauchn. Semin. POMI, 394, 33–139 (2011); J. Math. Sci., 188, No. 5, 490–550 (2013).
N. A. Vavilov and A. V. Stepanov, “Overgroups of semisimple groups,” Vestnik Samara State Univ., Ser. Nat. Sci., No. 3, 51–95 (2008).
E. Yu. Voronetsky, “Normality of the elementary subgroup in Sp(2,A), ” Zap. Nauchn. Semin. POMI, 443, 33–45 (2016).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 452, 2016, pp. 32–51.
Rights and permissions
About this article
Cite this article
Voronetsky, E.Y. Normalizers of Elementary Overgroups of Ep(2, A). J Math Sci 232, 610–621 (2018). https://doi.org/10.1007/s10958-018-3892-z
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-018-3892-z