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

Authors:	Jianguo Zha

Institution:	Department of Applied Mathematics, Tong Ji University Shanghai 200092, China

Abstract:	We determine all group homomorphisms SL_n(D) $->$ GL_n(E), where Dand E are division rings such that char D = char E and E isfinite-dimensional over its centre. Apart from the case wheren = 2 and D is F₂ or F_3, all non-trivial group homomorphismsSL_n(D) $->$ GL_n(E) are induced from homomorphisms and anti-homomorphismsD $->$ E.

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