On the coradical filtration of pointed coalgebras

Abstract

We investigate the coradical filtration of pointed coalgebras. First, we generalize a theorem of Taft and Wilson using techniques developed by Radford in [Rad78] and [Rad82]. We then look at the coradical filtration of duals of inseparable field extensions L * upon extension of the base field K, where K ⊆ L is a field extension. We reduce the problem to the case that the field extension is purely inseparable.

Quantum field theory meets Hopf algebra

“…As a consequence, if G(C) denotes the set of group-like elements of C, then the coradical C 0 of C is generated by the elements of G(C) and there is a coideal I of C such that C = C 0 ⊕ I and ε(I) = 0. Moreover, ε(g) = 1 for g ∈ G(C) (see [46], section 5.4 and [47]). Then, for any element g ∈ G(C) and u ∈ S(C), we define (g|u) = ε(u), so that ε(g • u) = ε(u) and g • u = gu.…”