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- W2942257426 abstract "We consider Hopfological techniques as in cite{Ko} but for infinite dimensional Hopf algebras, under the assumption of being co-Frobenius. In particular, $H=k[{mathbb Z}]#k[x]/x^2$ is the first example, whose corepresentations category is d.g. vector spaces. Motivated by this example we define the Homology functor (we prove it is homological) for any co-Frobenius algebra, with coefficients in $H$-comodules, that recover usual homology of a complex when $H=k[{mathbb Z}]#k[x]/x^2$. Another easy example of co-Frobenius Hopf algebra gives the category of mixed complexes and we see (by computing an example) that this homology theory differs from cyclic homology, although there exists a long exact analogous to the SBI-sequence. Finally, because we have a tensor triangulated category, its $K_0$ is a ring, and we prove a last part of a localization exact sequence for $K_0$ that allows us to compute -or describe- $K_0$ of some family of examples, giving light of what kind of rings can be categorified using this techniques." @default.
- W2942257426 created "2019-05-03" @default.
- W2942257426 creator A5058238788 @default.
- W2942257426 date "2019-04-23" @default.
- W2942257426 modified "2023-09-27" @default.
- W2942257426 title "Hopfological algebra for infinite dimensional Hopf algebras" @default.
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- W2942257426 hasPublicationYear "2019" @default.
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