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Results tagged with hopf-algebras
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user 11546
A Hopf algebra is a vector space $H$ over a field $k$ endowed with an associative product $\times:H\otimes_k H\to H$ and a coassociative coproduct $\Delta:H\to H\otimes_k H$ which is a morphism of algebras. Unit $1:k\to H$, counit $\epsilon:H\to k$ and antipode $S:H\to H$ are also required. Such a structure exists on the group algebra $k G$ of a finite group $G$.
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Hopf-Galois Structure Maps
A Hopf-Galois extension of commutative rings, as defined by Montgomery here, is a morphism of commutative rings $\phi:A\to B$ with a Hopf-algebra $H$ coacting on $B$ by a ring map $c:B\to B\otimes H$ …
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Hopf-Galois extensions where the "extension" is a module?
For $H$ a Hopf-algebra, an $H$-Hopf-Galois extension is a map of rings $\phi\colon\thinspace A\to B$ such that $H$ coacts on $B$ over $A$, $B\otimes_AB\cong B\otimes H$, and the cofixed points, or the …
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Accepted
Hopf-algebras in associative ring spectra
Okay, I'll take a crack at it, although this is basically just a translation of Tyler's comments from the chat room. Recall that given a topological group (or group like $A_\infty$-space) $A$, we can …
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Hopf-algebras in associative ring spectra
I'm interested in a definition of cocommutative Hopf-algebra objects in the $\infty$-category of associative (read: $A_\infty$) ring spectra. One thought I had was to think of cocommutative Hopf-algeb …
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6
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Topological quotient Hopf-algebras and "change-of-rings"
One way of constructing coalgebra objects in the homotopy theorist's category of spectra is to take the suspension spectrum of a space, with the diagonal providing a cocommutative comultiplication. If …
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