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Determination of Homomorphisms between Linear Groups of the same Degree over Division Rings
Author(s) -
Jianguo Zha
Publication year - 1996
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/53.3.479
Subject(s) - homomorphism , division (mathematics) , mathematics , division ring , group (periodic table) , degree (music) , char , pure mathematics , discrete mathematics , combinatorics , chemistry , arithmetic , physics , organic chemistry , acoustics , pyrolysis
We determine all group homomorphisms SL n ( D ) → GL n ( E ), where D and E are division rings such that char D = char E and E is finite‐dimensional over its centre. Apart from the case where n = 2 and D is F 2 or F 3, all non‐trivial group homomorphisms SL n ( D ) → GL n ( E ) are induced from homomorphisms and anti‐homomorphisms D → E .