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Results tagged with hopf-algebras
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user 22709
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 $G$.
1
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Geometric interpretation of integrals of coordinate rings
Just a quick answer: I have maybe slightly different Hopf algebras in mind as you, but in my applications the integral often behaves like the fundamental class of a manifold.
[Added as answer:] The …
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2
votes
Accepted
Dimension formula for Cartan-type abelian.group Nichols algebra?
Yes, careful application of the theory of rootsystems verifies indeed these formulae.....farily streight-forward!
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2
votes
0
answers
68
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2-cocycles/Bigalois-objects over nontrivial liftings
It is easy to extend group-2-cocycles to smash-products with Nichols algebras over the group (just trivially). The same certainly doesn't work for nontrivial liftings.
As I would like to check a cons …
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6
votes
1
answer
219
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Liftings of Nichols algebras over racks via Doi twist
As a more nontrivial example for my Dissertation thesis, I'd require some example of the following type (of course I'll "cite" ;-) ), so thanx in advance:
Andruskiewitsch/Grana have by a new construc …
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6
votes
1
answer
230
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Dimension formula for Cartan-type abelian.group Nichols algebra?
Existence of a root system has been established for Nichols algebras $B(V)$ of a Yetter-Drinfel'd-module $V$ (resp. braided vectorspaces $V$) over abelian groups (resp. with diagonal braiding $x_i\oti …
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10
votes
Accepted
2-cocycle twists of braided Hopf algebras
The two concepts - twisting a Hopf algebra one-sided to an algebra and two-sided to a new Hopf algebra - are actually intimately connected and play an important role in several areas of current resear …
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0
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Finding the Universal Ideal of a (Covariant) Differential Calculus
I don't much about differential calculi, but back in my head I also remember somewhat like this....so as a HINT (?): Could N be the kernel of something like a "quantum shuffle map" or "quantum symmetr …
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12
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Tensor product of linear mappings versus chain complexes
Even at the risk of using slightly too heavy armory, I would like to shortly explain, how I would view the situation in a light, that naturally produces and "explains" the observations collected above …
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