Dear Chhatramani,
   This is a project that is heavily based on algebraic foundations that 
requires an understanding of many subtle behaviors that are not necessarily 
present in cluster algebras because of the q-commuting variables. I should 
also caution that when I say "reading research papers", there is an 
implication that you can understand and extract information that is 
relevant, which requires understanding the necessary algebra. This project 
also is tightly related to combinatorics as you probably surmised from the 
literature. Some other papers on more recent developments for quantum 
cluster algebras that are likely to be useful are

[1] - https://arxiv.org/abs/1602.00498
[2] - https://arxiv.org/abs/1309.7869
[3] - https://arxiv.org/abs/0912.4397
[4] - https://arxiv.org/abs/1206.3586

This is a relatively new mathematical object to study, so there are not any 
good survey papers that I am aware of on this subject.

Something that would be good to have would be the quantum Grassmannians of 
Grabowski and Launois [2]. This could be implemented as a subalgebra of the 
quantum matrix coordinate algebra; at least, that is the easiest way I 
could see it done. This would be a good way to get yourself familiar with 
making contributions to Sage.

Best,
Travis


On Tuesday, March 13, 2018 at 1:21:35 AM UTC+10, Chhatramani S 5-Yr IDD 
Metallurgical Engg. wrote:
>
> Dr Travis Scrimshaw 
>                                  I am following this project idea for some 
> time now. I am from IIT(BHU) pursuing my IDD(B.tech+M.tech degree) in 
> metallurgical engineering, right now i am working on my master thesis on 
> computational metallurgy. I am a profound knowledge of C++ and 
> python(worked on some research projects ). I have already setup sage in my 
> laptop and completed the tutorial and I have studied linear algebra in my 
> university.I have watched lecture on Quantum Dilogarithms and Quantum 
> Cluster Algebra <https://www.youtube.com/watch?v=fkG1bz9818M&t=60s> . I 
> have read some research papers on Quantum cluster algebras(Advances in 
> Mathematics 195, Arkady Berenstein, Andrei Zelevinskyb(2005),CLUSTER 
> ALGEBRAS: AN INTRODUCTION(LAUREN K. WILLIAMS) 
> <https://math.berkeley.edu/~williams/papers/CA.pdf>) and the references 
> given in cluster seed documentary, right now i am reading the compendium on 
> cluster algebra and quiver package in sage and your documentation on Quantum 
> matrix coordinate algebras 
> <http://www.google.com/url?q=http%3A%2F%2Fdoc.sagemath.org%2Fhtml%2Fen%2Freference%2Falgebras%2Fsage%2Falgebras%2Fquantum_matrix_coordinate_algebra.html&sa=D&sntz=1&usg=AFQjCNEFXmua9yVsuRN6NH73X2LQ1RqiHA>.
>  
> I am comfortable in reading research material on following topic as i 
> am experienced in reading research papers. can you give some more 
> references on quantum cluster algebras and I am a bit delayed because of 
> some of my personal issues, i will forward you the basic implementation in 
> 2/3 days. 
>        thank you,
>      
>
> please give any remark/ feedback that will help in implementation of 
> quantum cluster algebra
>
>

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