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Homology Isomorphisms Between Algebraic Groups Made Discrete
Author(s) -
Dwyer William G.,
Jekel Solomon M.,
Suciu Alexander I.
Publication year - 1993
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/25.2.145
Subject(s) - mathematics , library science , sociology , mathematics education , algebra over a field , computer science , pure mathematics
Let $\Gamma$ be a connected, affine algebraic group over a field of characteristic 0, and $G$ its unipotent radical. Assume there is a central element in $\Gamma/G$ that induces a diagonalizable endomorphism in each lower central series quotient $G_i/G_{i+1}$, with all eigenvalues rational and greater than 1. Then, the projection $\Gamma^\delta\to (\Gamma/G)^\delta$ induces an isomorphism $H_*(\Gamma^\delta;\Z) \to H_*((\Gamma/G)^\delta;\Z)$.