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Results tagged with coalgebras
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user 161009
For questions about coalgebras, comultiplication, cocommutativity, counity, comodules, bicomodules, coactions, corepresentations, cotensor product, subcoalgebras, coideals, coradical, cosemisimplicity, ...
2
votes
1
answer
57
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Coradical filtration for comodules is exhaustive
It is a standard fact in the theory of coalgebras and comodules that, given a coalgebra $C$ and a comodule $M$ over $C$, the coradical filtration
$$M_n := \Delta^{-1}(M\otimes C_0 + M_{n-1}\otimes C)$$ … In a similar vein, would anyone have a suggestion for a good introductory text on coalgebras I could recommend to a student? …
- 518
6
votes
1
answer
353
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Comparing Hochschild (co)homology for algebras and coalgebras
Given a field $k$, an associative $k$-algebra $A$, and an $A$-bimodule $M$, one can define as the Hochschild homology and cohomology as the homology of the complexes
$$M\otimes A^{\otimes n}$$
and
$$\ …
- 518
2
votes
Comparing Hochschild (co)homology for algebras and coalgebras
We assume $A$ and $M$ are finite dimensional, and denote by $A*$ and $M*$ their respective duals. Denote by $HH_n$ and $CH_n$ the Hochschild homology of an algebra and a coalgebra respectively, and si …
- 518