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Results tagged with operads
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user 109
7
votes
Accepted
GL(V)-representation theory for a Lie bracket kernel
The representations are not in general irreducible. The second characterisation is the more useful to my mind because one can decompose $Lie((n+2))$ as an $Sym(n+2)$-module, which gives a decompositi …
- 1,680
4
votes
What are operad automorphisms?
[EDIT] (just restating Ryan's comment on the original post)
An operad endomorphism is an operad morphism where the source and target operads are the same. …
- 1,680
5
votes
Accepted
Operad terminology - Operads with and without O(0).
I can second Jeffrey's comment, reduced is used to say that O(1) is just the monoidal unit (it allows us to use the Boardman Vogt resolution in homotopy theory). It's my opinion that this terminology …
- 1,680
8
votes
Shuffle Hopf algebra: how to prove its properties in a slick way?
I have come across a nice way to think about this Hopf algebra. Let $v_1\otimes\ldots\otimes v_n$ be a monomial in $TV$. Rather than thinking of it as just a word, think of it as a path of $n$ steps …
- 1,680
6
votes
Shuffle Hopf algebra: how to prove its properties in a slick way?
I believe the right way to consider this algebra is to view it as the free zinbiel algebra. A zinbiel algebra has a single operation o which must satisfy
(x o y) o z = x o (y o z + z o y)
The zinbi …
- 1,680