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Results tagged with hopf-algebras
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user 750
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 $G$.
38
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6
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Why Drinfel'd-Jimbo-type quantum groups?
Hopf algebras are pretty easy to motivate, as a not-necessarily-commutative generalization of the ring of functions on an algebraic group (and there are many other ways in which they come up). I like …
- 63.9k
6
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Why Drinfel'd-Jimbo-type quantum groups?
So, here's some of my own investigation into this. Define the n-th partial flag variety $Fl_n(\mathbb{C}^m)$ to be the set of all n-step partial flags
$$F_0 \subseteq F_1 \subseteq ... \subseteq F_n …
- 13k