; TeX output 1995.12.06:0928|7 N;*N cmbx12SYMMETRICٚYETTER-DRINFELDCATEGORIESARETRIVIAL pK`y cmr10BODOUUP*AREIGIS#XQ cmr12NorvembSer27,1995WVeoshorwthefollowingtheoremansweringaquestionofS.MontgomeryandD.Fiscrhman.Theorem.PY+@ cmti12Lffetn$g cmmi12H[beakg-Hopfalgebrasuchthatthecanonicalbraidingofthecategory%!", cmsy10YD2UV2cmmi8HRAH of35Yetter-Drinfeldmoffdulesisasymmetry.fiThenHB=URkg.Prffoof.6LetM6:=URHwiththecoregularcoSoperationofHastheHV-comoSdulestructure(s2(h)UR=u cmex10Ph|{Ycmr81z vh2)andwiththeadjoinrtopSerationofHyonitselfasmodulestructure(xuhQ=PS(h1)xh2).Then@MV$isaYVetter-DrinfeldmoSduleoracrossedmodule,i.e. |ayrighrtHV-moSduleandarightHV-comoSdulesuchthatP(xth)0zx (xh)1 =ȟPo(x0jh2) S(h1)x1h3.LetXN6:=URHwiththeregularopSerationofHonitselfasmoSdulestructure(xT;hUR=xh)uQandthecoadjoinrtcoSoperationuQofHbastheHV-comoSdulestructure(s2(h)UR=Ph2z S(h1)h3).8ThenN+isaYVetter-DrinfeldmoSdule.ApplythesquareofthebraidingW(x6< yn9)UR=Py0@ 6