特殊酉群(special unitary group)酉群的一个重要子群.酉群Un(K,f)的子群U.,(K,f) (}SL.,(K)称为特殊酉群,记为SU?(K,f). U(n)的特殊酉群记为SU(n).若U?(K,f)不是正交群,f是迹形式且指数)1,则Un(K,f)含有平延,称为酉平延.此时U?(K,f)中全体酉平延生成一个正规子群T?(K,f>,称为酉平延群.若K交换,则除U?(K,f)一U3(F4,f)的情形外,Tn(K,f)=SUn(K,f).当Un(K,f)是辛群时酉平延改称辛平延,此时Tn(K,f)=Sp?(K,f). SUn(K,f)和T?(K,f)在自然同态GI_n (K ) }PGLn (K)下的像PSUn (K , f)和PTn (K,f)分别称为射影特殊酉群和射影酉平延群