02481nam a22003735a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084003600185100003100221245008000252260008200332300003400414336002600448337002600474338003600500347002400536490005100560506006600611520116500677650003401842650004001876650002301916650002801939650004301967856003202010856006502042172-140124CH-001817-320140124234500.0a fot ||| 0|cr nn mmmmamaa140124e20140118sz fot ||| 0|eng d a978303719630470a10.4171/1302doi ach0018173 7aPBFD2bicssc a13-xxa05-xxa14-xxa17-xx2msc1 aMarsh, Robert J.,eauthor.10aLecture Notes on Cluster Algebrash[electronic resource] /cRobert J. Marsh3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2014 a1 online resource (121 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aZurich Lectures in Advanced Mathematics (ZLAM)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aCluster algebras are combinatorially defined commutative algebras which were introduced by S. Fomin and A. Zelevinsky as a tool for studying the dual canonical basis of a quantized enveloping algebra and totally
positive matrices. The aim of these notes is to give an introduction to cluster algebras which is accessible to graduate students or researchers interested in learning more about the field, while giving a taste of the
wide connections between cluster algebras and other areas of mathematics.
The approach taken emphasizes combinatorial and geometric aspects of cluster algebras. Cluster algebras of finite type are classified by the Dynkin diagrams, so a short introduction to reflection groups is given in
order to describe this and the corresponding generalized associahedra. A discussion of cluster algebra periodicity, which has a close relationship with discrete integrable systems, is included. The book ends with a
description of the cluster algebras of finite mutation type and the cluster structure of the homogeneous coordinate ring of the Grassmannian, both of which have a beautiful description in terms of combinatorial
geometry.07aGroups & group theory2bicssc07aCommutative rings and algebras2msc07aCombinatorics2msc07aAlgebraic geometry2msc07aNonassociative rings and algebras2msc40uhttps://doi.org/10.4171/130423cover imageuhttps://www.ems-ph.org/img/books/marsh_mini.jpg