Determination of Homomorphisms between Linear Groups of the same Degree over Division Rings | Zendy

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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 .

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