TY - JOUR
T1 - SAMELSON PRODUCTS in p-REGULAR SO(2n) and ITS HOMOTOPY NORMALITY
AU - Kishimoto, Daisuke
AU - Tsutaya, Mitsunobu
N1 - Publisher Copyright:
© 2017 Glasgow Mathematical Journal Trust.
PY - 2018/1/1
Y1 - 2018/1/1
N2 - A Lie group is called p-regular if it has the p-local homotopy type of a product of spheres. (Non)triviality of the Samelson products of the inclusions of the factor spheres into p-regular SO(2n (p) is determined, which completes the list of (non)triviality of such Samelson products in p-regular simple Lie groups. As an application, we determine the homotopy normality of the inclusion SO(2n-1) → SO(2n) in the sense of James at any prime p.
AB - A Lie group is called p-regular if it has the p-local homotopy type of a product of spheres. (Non)triviality of the Samelson products of the inclusions of the factor spheres into p-regular SO(2n (p) is determined, which completes the list of (non)triviality of such Samelson products in p-regular simple Lie groups. As an application, we determine the homotopy normality of the inclusion SO(2n-1) → SO(2n) in the sense of James at any prime p.
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U2 - 10.1017/S001708951600063X
DO - 10.1017/S001708951600063X
M3 - Article
AN - SCOPUS:85011876841
SN - 0017-0895
VL - 60
SP - 165
EP - 174
JO - Glasgow Mathematical Journal
JF - Glasgow Mathematical Journal
IS - 1
ER -