What is a Taft algebra? Is there any references about the original conception?
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$\begingroup$ In what context did you come across them? Googling "taft algebra" tells me pretty quickly that they have something to do with Hopf algebras. Please be more specific, and try to come up with a version of this question that's either a bit more specific or a bit more motivated. $\endgroup$– Yemon ChoiCommented Apr 16, 2010 at 6:44
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$\begingroup$ OK,thank you. We can use quiver to define a Hopf algebra. And with some special condition, it will be isomorphic to the taft algebra. So, my quetion is that I know nothing about the taft algebra. I want to refer a paper introducing about taft algebra in detail. $\endgroup$– RubyCommented Apr 16, 2010 at 6:53
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2$\begingroup$ As noted, the question is about Hopf algebras and needs such a tag. The concept originates with work of Earl Taft (retired from Rutgers) and began to show up in arXiv preprints such as math.QA/0009214. But to get back to the origins one should search earlier using MathSciNet if possible. Searches on Google, Wikipedia, or even arXiv are probably too limited for this purpose. $\endgroup$– Jim HumphreysCommented Apr 16, 2010 at 11:41
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1$\begingroup$ Retagged. Ruby, you may want to go edit your original question to include what you have in the above comment, and more if possible. $\endgroup$– Cam McLemanCommented Apr 16, 2010 at 13:26
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1 Answer
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See the original article
http://www.pnas.org/content/68/11/2631.full.pdf
or any textbook on Hopf algebras. These were first examples of neither commutative, nor cocommutative Hopf algebras.
Taft algebras show up in classification of finite-dimensional non-semisimple Hopf algebras. For instance, it is known that any non-semisimple Hopf algebra of dimension $p^2$, $p$ is prime, over algebraically closed field of characteristic zero is isomorphic to a Taft algebra.