"Monoidal categorifications of cluster algebras"의 두 판 사이의 차이

2011년 4월 13일 (수) 05:08 판

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

\thm (Gabriel)

A connected quiver Q has finite type iff corresponding graph is Dynking diagram (A,D,E)

outline of a proof of the periodicity conjecture for pairs of Dynkin diagrams

Keller, Bernhard. 2008. “Cluster algebras, quiver representations and triangulated categories”. 0807.1960 (7월 12). [1]http://arxiv.org/abs/0807.1960.
Cluster algebras, quiver representations
Total positivity, cluster algebras and categorification

Caldero, Philippe, 와/과Andrei Zelevinsky. 2006. “Laurent expansions in cluster algebras via quiver representations”. math/0604054 (4월 3). http://arxiv.org/abs/math/0604054.

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 <h5>expositions</h5>
-* Keller, Bernhard. 2008. “Cluster algebras, quiver representations and triangulated categories”. <em>0807.1960</em> (7월 12). 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, quiver representations
 * [http://www.mpim-bonn.mpg.de/node/365 Total positivity, cluster algebras and categorification]
@@ 108번째 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>
-*   <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/과Frederic Chapoton. 2004. “Cluster algebras as Hall algebras of quiver representations”. <em>math/0410187</em> (10월 7). http://arxiv.org/abs/math/0410187.<br>  <br>
 * http://www.ams.org/mathscinet
 * http://www.zentralblatt-math.org/zmath/en/