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March 20, 2007

Generalising Hopf Algebras

Posted by David Corfield

To prepare for the appearance of categorified quantum groups it might be worth taking a look at Gizem Karaali’s On Hopf Algebras and Their Generalizations, in which she describes Hopf algebras and five attempts to generalise them. Much hangs on their representation categories.

Hopfish algebras are briefly touched on. As I noted in the Oct 21 entry of my old blog, according to Alan Weinstein and colleagues,

We call our new objects hopfish algebras, the suffix “oid” and prefixes like “quasi” and “pseudo” having already been appropriated for other uses. Also, our term retains a hint of the Poisson geometry which inspired some of our work.

Posted at March 20, 2007 1:48 PM UTC

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3 Comments & 0 Trackbacks

Re: Generalising Hopf Algebras

One correction needed: Gizem is female.

Posted by: A.J. on March 20, 2007 5:19 PM | Permalink | Reply to this

Re: Generalising Hopf Algebras

Thanks very much for noticing that. I’ll correct it.

Posted by: David Corfield on March 20, 2007 5:28 PM | Permalink | Reply to this

Re: Generalising Hopf Algebras

So, does this generalize when you categorify, to infinite dimensional?

http://arxiv.org//pdf/math.RA/0703601

Title: Classification of pointed rank one Hopf algebras
Authors: Sarah Scherotzke
Comments: 22 pages
Subj-class: Rings and Algebras
MSC-class: 16W30

In this paper we classify the finite-dimensional pointed rank one Hopf algebras which are generated as algebras by the first element of the coradical filtration over a field of prime characteristic.

Posted by: Jonathan Vos Post on March 21, 2007 6:02 PM | Permalink | Reply to this

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