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Results tagged with coalgebras
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user 2530
For questions about coalgebras, comultiplication, cocommutativity, counity, comodules, bicomodules, coactions, corepresentations, cotensor product, subcoalgebras, coideals, coradical, cosemisimplicity, ...
0
votes
Accepted
How is the coradical filtration defined?
I am voting to close this. $C_n$ should be defined as $\Delta^{-1}\left(C\otimes C_0+C_{n-1}\otimes C\right)$. My wrong definition was due to my bad memory. Sorry for spamming.
- 33.8k
5
votes
Is there an explicit construction of a free coalgebra?
I have but briefly skimmed the contents of this paper (Michiel Hazewinkel, Cofree coalgebras and multivariable recursiveness, Journal of Pure and Applied Algebra, Volume 183, Issues 1--3, 1 September 2003 …
- 33.8k
2
votes
Accepted
Linear functional kills all primitives of a connected filtered coalgebra => it lies in m^2?
.$ be graded coalgebras (I use the square brackets in $C_{\left[ n\right] }$ to distinguish it from an $n$-th graded component of something). … Instead, we can define a "connected graded sum" of connected graded coalgebras $C_{\left[ 1\right] } $, $C_{\left[ 2\right] }$, $C_{\left[ 3\right] }$, $...$ as follows:
Consider the direct sum …
- 33.8k
7
votes
Accepted
Problem with Eisenbud's Lemma "Symmetry of Diagonalization"?
I think this is a mistake in Eisenbud's book.
It seems, however, that Eisenbud only uses Lemma A2.5 in two places: in the proof of Proposition A2.4, and in the proof of Proposition-Definition A2.6.
…
- 33.8k
2
votes
Accepted
Connected graded involutive bialgebras (Hopf algebras) sought (for Dynkin idempotent checking)
The answers to both the Concrete Question and the analogous question for $\log\operatorname*{id}$ are "No". By that I mean that now I am sufficiently convinced of the correctness of my Sage 5.0 code. …
- 33.8k