Notation Tables

Algebra

Notation	Usage
$(H, \nabla, e, Δ, ϵ, κ)$	A Hopf algebra over a field $K$ .
$H$	The vector space underlying a Hopf algebra.
$K$	The base field for the vector space $H$ .
$\nabla : H \otimes H \to H$	The product on a Hopf algebra.
$e : K \to H$	The unit of a Hopf algebra.
$Δ : H \to H \otimes H$	The coproduct on a Hopf algebra.
$ϵ : H \to K$	The counit of a Hopf algebra.
$κ : H \to H$	The antipode of a Hopf algebra.
$1_{K} \in K$	This is the multiplicative identity in $K$ .
$1 \in H$	This is the "identity" in $H$ . That is, $1 = e (1_{K})$ .
$0_{K} \in K$	This is the additive identity in $K$ .
$0 \in H$	This is $e (0_{K})$ .
$G (H) \subseteq H$	This is the group of group-like elements of a Hopf algebra $H$ .
$P (H) \subseteq H$	This is the Lie algebra of primitive elements of a Hopf algebra $H$ .