On Faithful Representations of Lie Groups
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چکیده
where tE:R and I is the unit matrix of degree d. Let GL(K, d) denote the group of all nonsingular matrices of degree d with coefficients in K. Any subgroup of GL(K, d) will be called a linear group of degree d. Let 0 be the identity representation of a linear Lie group G with the Lie algebra 8 so that 9(x) =x (*EG). Then dd is a faithful representation of g and exp dd(X) =0(exp X) =exp X for any x£.q. Hence we may identify 8 with dß{%) under dd. 8 can therefore be regarded as a linear Lie algebra. In particular the Lie algebra of GL(R~, d) then
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تاریخ انتشار 2010