A class of Hopf module structure characterizations

yxfbbiedtj · Wysłany: Śro 8:45, 30 Mar 2011

A class of Hopf module structure characterizations

Is the H- mode with the state , Va ~ b ∈ H0H, there are (id0g) ( port o6) = ag (b). If b ∈ J, then there is ag (b) = (b) = f (ab) = g (ab) = grn ( mouth ob); if bJ, then there is ag (b) aO = 0, and gm ( oral ob ) = g (ab) = 0, and if not , g () ≠ 0, then there is g () = f (ab) = gamma (oral ob) = (id0m) ( port ob) = af (b), since b Report J, so f (b) meaningless , so g (ab) ≠ factory (), thus g () = 0. By a linear expansion of the known (id0g) = gm, so g is the H- mode with the state. So we know that M is injective. To further analyze the structural properties of M -mode , the following model structure on M, mapping analysis, the Hopf algebra H is commutative , the HoH is exchanged . Lemma 4 Let N be left H_ module, then N is a model of left H0H . Prove that the definition of = (moid), is clearly a K with state , take any ∈ N, mouth , 6, c, d ∈ H, (idoido) (a ~ bocoo) = (a ~ boo (co0)) = (a ~ b0 (cdm)) = abcdn; and ( brain Hoid) (a ~ bocoo) = ~ o (acobdo) = (aC) (bd) = abcdn = (idOid0) (a ~ boc0o). -8 * Guangxi Normal University ( Natural Science) 23 ( Pa H) ( a t /) = kg (1H1H) = kn = is. Shows the linear expansion of ( Pa Hid) = (idid) and ( the Hid) = id. Therefore, N is 7 . . HQH a mold . Thus we have the following proposition Proposition 2 When H is commutative Hopf algebra is a left module homomorphisms HOH . Proof of Lemma 1 and Lemma 4 we can see , MOH and M are the left- HH a mold , respectively, and its structure map . Take any port , b, c ∈ H, (h,) ∈ M, (idid) (a ~ b (,) c) = ( port 6 (, xc)) = (h, abxc), and , ( Port 6 (h,) c) = ( port (h,) bc) = (h,[link widoczny dla zalogowanych], axbc) = (h, abxc), so (id ~ id) ( port 6 (,) c) = neigh ( port 6 (,) c). We can see the cries of the linear expansion = (id / d). Therefore, a model with the left H0H state.