TY - JOUR
ID - 331
TI - CLUSTER ALGEBRAS AND CLUSTER CATEGORIES
JO - Bulletin of the Iranian Mathematical Society
JA - BIMS
LA - en
SN - 1017-060X
AU - KELLER, B.
AD -
Y1 - 2011
PY - 2011
VL - 37
IS - No. 2
SP - 187
EP - 234
KW - Cluster algebra
KW - quiver representation
KW - cluster category
KW - triangulated category
DO -
N2 - These are notes from introductory survey lectures given
at the Institute for Studies in Theoretical Physics and Mathematics
(IPM), Teheran, in 2008 and 2010. We present the definition and
the fundamental properties of Fomin-Zelevinsky’s cluster algebras.
Then, we introduce quiver representations and show how they can
be used to construct cluster variables, which are the canonical generators
of cluster algebras. From quiver representations, we proceed
to the cluster category, which yields a complete categorification of
the cluster algebra and its combinatorial underpinnings.
UR - http://bims.iranjournals.ir/article_331.html
L1 - http://bims.iranjournals.ir/article_331_d4a48fe4c80e61417522a29c539ecce5.pdf
ER -