"Monoidal categorifications of cluster algebras"의 두 판 사이의 차이
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<h5>Caldero-Chapoton formula</h5> | <h5>Caldero-Chapoton formula</h5> | ||
| − | + | CC(V) =\chi_{V} | |
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* Keller, Bernhard. 2008. “Cluster algebras, quiver representations and triangulated categories”. <em>0807.1960</em> (7월 12). [http://arxiv.org/abs/0807.1960. ]http://arxiv.org/abs/0807.1960. | * Keller, Bernhard. 2008. “Cluster algebras, quiver representations and triangulated categories”. <em>0807.1960</em> (7월 12). [http://arxiv.org/abs/0807.1960. ]http://arxiv.org/abs/0807.1960. | ||
| − | * Cluster algebras | + | * [http://www.math.jussieu.fr/%7Ekeller/publ/Reisensburg.pdf Cluster algebras and quiver representations], Keller, Bernhard, 2006 |
* [http://www.mpim-bonn.mpg.de/node/365 Total positivity, cluster algebras and categorification] | * [http://www.mpim-bonn.mpg.de/node/365 Total positivity, cluster algebras and categorification] | ||
| 109번째 줄: | 109번째 줄: | ||
<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">articles</h5> | <h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">articles</h5> | ||
| + | * Rupel, Dylan. 2010. “On Quantum Analogue of The Caldero-Chapoton Formula”. <em>1003.2652</em> (3월 12). doi:doi:10.1093/imrn/rnq192. http://arxiv.org/abs/1003.2652.<br> <br> | ||
* Caldero, Philippe, 와/과Andrei Zelevinsky. 2006. “Laurent expansions in cluster algebras via quiver representations”. <em>math/0604054</em> (4월 3). http://arxiv.org/abs/math/0604054. | * Caldero, Philippe, 와/과Andrei Zelevinsky. 2006. “Laurent expansions in cluster algebras via quiver representations”. <em>math/0604054</em> (4월 3). http://arxiv.org/abs/math/0604054. | ||
| − | + | * Caldero, Philippe, 와/과Frederic Chapoton. 2004. “Cluster algebras as Hall algebras of quiver representations”. <em>math/0410187</em> (10월 7). http://arxiv.org/abs/math/0410187. | |
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* http://www.ams.org/mathscinet | * http://www.ams.org/mathscinet | ||
* http://www.zentralblatt-math.org/zmath/en/ | * http://www.zentralblatt-math.org/zmath/en/ | ||
2011년 4월 13일 (수) 05:13 판
introduction
- replace cluster variables by modules
notions
- quiver : oriented graph
- represetation of a quiver : collection of vector space and linear maps between them
- homomorphism of 2 quiver representations
- path algebra of a quiver
- given a quiver Q, a path p is a sequence of arrows with some conditions
- path algebra : set of all k-linear combinations of all paths (including e_i's)
- p_1p_2 will correspond to a composition \(p_2\circ p_1\) of two maps (\(U\overset{P_2}{\rightarrow }V\overset{P_1}{\rightarrow }W\))
- quiver representation is in fact, a representaion of path algebra of a quiver
finite type quiver classfication
- quiver has finite type of there are finitely many indecomposables
\thm (Gabriel)
A connected quiver Q has finite type iff corresponding graph is Dynking diagram (A,D,E)
Caldero-Chapoton formula
CC(V) =\chi_{V}
periodicity conjecture
outline of a proof of the periodicity conjecture for pairs of Dynkin diagrams
history
encyclopedia
- http://en.wikipedia.org/wiki/
- http://www.scholarpedia.org/
- http://eom.springer.de
- http://www.proofwiki.org/wiki/
- Princeton companion to mathematics(Companion_to_Mathematics.pdf)
books
expositions
- Keller, Bernhard. 2008. “Cluster algebras, quiver representations and triangulated categories”. 0807.1960 (7월 12). [1]http://arxiv.org/abs/0807.1960.
- Cluster algebras and quiver representations, Keller, Bernhard, 2006
- Total positivity, cluster algebras and categorification
articles
- Rupel, Dylan. 2010. “On Quantum Analogue of The Caldero-Chapoton Formula”. 1003.2652 (3월 12). doi:doi:10.1093/imrn/rnq192. http://arxiv.org/abs/1003.2652.
- Caldero, Philippe, 와/과Andrei Zelevinsky. 2006. “Laurent expansions in cluster algebras via quiver representations”. math/0604054 (4월 3). http://arxiv.org/abs/math/0604054.
- Caldero, Philippe, 와/과Frederic Chapoton. 2004. “Cluster algebras as Hall algebras of quiver representations”. math/0410187 (10월 7). http://arxiv.org/abs/math/0410187.
- http://www.ams.org/mathscinet
- http://www.zentralblatt-math.org/zmath/en/
- http://arxiv.org/
- http://www.pdf-search.org/
- http://pythagoras0.springnote.com/
- http://math.berkeley.edu/~reb/papers/index.html
- http://dx.doi.org/
question and answers(Math Overflow)
- http://mathoverflow.net/search?q=
- http://mathoverflow.net/search?q=
- http://math.stackexchange.com/search?q=
- http://math.stackexchange.com/search?q=
blogs
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experts on the field