To end the semester . . .
I just wanted to share this picture. (I took this picture earlier last week at Rosamunde in San Francisco.) Happy end of semester to everyone. Cheers!
To end the semester . . .
I just wanted to share this picture. (I took this picture earlier last week at Rosamunde in San Francisco.) Happy end of semester to everyone. Cheers!
Class Notes
Hello everyone, I TeX’d up a bunch of notes from the lectures and lecture notes and thought others might be interested in getting a copy of them. Use with caution – these notes are not complete and there may be
Class Notes
Hello everyone, I TeX’d up a bunch of notes from the lectures and lecture notes and thought others might be interested in getting a copy of them. Use with caution – these notes are not complete and there may be
Hopfication sensation across the nation
We have said that non-finite dimensional Hopf algebras may not have a linear dual, but that if they are graded we can fake it with a graded dual. For the non-graded case, how much information is lost if we define
Hopfication sensation across the nation
We have said that non-finite dimensional Hopf algebras may not have a linear dual, but that if they are graded we can fake it with a graded dual. For the non-graded case, how much information is lost if we define
group of characters
In our lecture notes, it says that the group of characters of a hopf algebra is the set of algebra maps from H to k.The operation of this group is the convolution product which is related to the algebra’s coproduct. Do the
group of characters
In our lecture notes, it says that the group of characters of a hopf algebra is the set of algebra maps from H to k.The operation of this group is the convolution product which is related to the algebra’s coproduct. Do the
Two important comments on the scalar product
1. Again, please note the mistake I made in class and on the lecture notes. I am about to correct the notes and reupload them: https://hopfcombinatorics.wordpress.com/2012/04/26/latex-se_lambda-1n-h_lambda-and-a-mistake-in-lecture-3/ 2. The inner product on Sym has the very nice property that it is
Two important comments on the scalar product
1. Again, please note the mistake I made in class and on the lecture notes. I am about to correct the notes and reupload them: https://hopfcombinatorics.wordpress.com/2012/04/26/latex-se_lambda-1n-h_lambda-and-a-mistake-in-lecture-3/ 2. The inner product on Sym has the very nice property that it is
S(e_n) = (-1)^n h_n, and a mistake in lecture
1. In class I explained that for any partition of , and that this follows from the equation for . Can someone provide a proof of this? (Hint: there are elegant formulas for the generating functions and .) 2. I made
S(e_n) = (-1)^n h_n, and a mistake in lecture
1. In class I explained that for any partition of , and that this follows from the equation for . Can someone provide a proof of this? (Hint: there are elegant formulas for the generating functions and .) 2. I made
Dominance order
Today in class I claimed that the transition matrix from the elementary symmetric functions to the monomial symmetric functions is upper triangular. However, it is not trivial to decide what order the rows and columns of this matrix should be
Dominance order
Today in class I claimed that the transition matrix from the elementary symmetric functions to the monomial symmetric functions is upper triangular. However, it is not trivial to decide what order the rows and columns of this matrix should be
Takeuchi’s Formula Vs. the Hopf Algebra diagram
I believe I was able to compute the antipode of G with help from a very patient classmate using the Hopf Algebra diagram. But in Federico’s office hours he suggested that it would be easier to use Takeuchi’s formula. I
Takeuchi’s Formula Vs. the Hopf Algebra diagram
I believe I was able to compute the antipode of G with help from a very patient classmate using the Hopf Algebra diagram. But in Federico’s office hours he suggested that it would be easier to use Takeuchi’s formula. I
Resources for flat graph algebras
Hey everyone. I found the following papers and lecture that pertain to flat graph algebras. Hope you find them as useful as I did. Dejan Delić “Finite Bases for Flat Graph Algebras” Journal of Algebra 2002 William A Lampe “Full
Resources for flat graph algebras
Hey everyone. I found the following papers and lecture that pertain to flat graph algebras. Hope you find them as useful as I did. Dejan Delić “Finite Bases for Flat Graph Algebras” Journal of Algebra 2002 William A Lampe “Full
Short HW 1
Problem 1 part d Silly question: What is the formula of the antipode for simple graphs and should we use Schmitts or this new formula suggested in this paper http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&ved=0CC8QFjAB&url=http%3A%2F%2Fwww.dmtcs.org%2Fdmtcs-ojs%2Findex.php%2Fproceedings%2Farticle%2Fdownload%2FdmAO0146%2F3596&ei=kBWOT5HpPKaYiQKN6PGDDw&usg=AFQjCNFZhp2LR4Yo8iRDu4lB3ugtjuIKkA? Thank you! 🙂
Short HW 1
Problem 1 part d Silly question: What is the formula of the antipode for simple graphs and should we use Schmitts or this new formula suggested in this paper http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&ved=0CC8QFjAB&url=http%3A%2F%2Fwww.dmtcs.org%2Fdmtcs-ojs%2Findex.php%2Fproceedings%2Farticle%2Fdownload%2FdmAO0146%2F3596&ei=kBWOT5HpPKaYiQKN6PGDDw&usg=AFQjCNFZhp2LR4Yo8iRDu4lB3ugtjuIKkA? Thank you! 🙂
hopf algebras and combinatorics 