5
votes
Accepted
Categorical description of umbral calculus?
An overview of the categorical description of umbral calculus is given by Nigel Ray, in
Universal Constructions in Umbral Calculus (1996).
The most flexible basis for the study of umbral calculus ...
- 188k
2
votes
Accepted
The shuffle algebra over the rationals is isomorphic to the polynomial algebra in the Lyndon words
This is proven in Theorem 6.3.4 of Hopf Algebras in Combinatorics
by Grinberg and Reiner.
They call it "Radford’s theorem on the shuffle algebra" citing Theorem 3.1.1(e) of A natural ring ...
- 7,875
1
vote
Accepted
Is Leray's theorem on commutative Hopf algebras proven in Milnor-Moore?
I forgot to give this question some closure. Basically, it was answered by @JohnPalmieri in his comment; let me just expand this answer.
The proof of Proposition 4.17 in the Milnor/Moore paper [B] is ...
- 33.8k
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