Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type VII. Semisimple classes in PSL(q) and PSp2(q)

Duality for infinite-dimensional braided bialgebras and their (co)modules

“…so that Ψ U H is also compatible with the multiplication on U . By Lemma 2.4, Ψ −1 HH is compatible with the comultiplication on H. Similar as above, (5). By Lemma 2.4 and the second relation of (11),…”

“…This implies (5), and (6) follows from ε {2} (a) v {1} (94) = ε(a {1} ) v {2} (11) = ε(a) v since ε yields the unit element in dual algebra U ⊂ H ′ .…”

“…Presumably the most prominent examples are infinite-dimensional Nichols algebras generated by a finite-dimensional Yetter-Drinfeld module (see e.g. [1,2,4,3,5,6,8,9]). For a convenient PBW basis, [15] may be consulted.…”