Total positivity and cluster algebras

By Sergey Fomin. 2010

79 citations recorded by the source corpus.

This is a brief and informal introduction to cluster algebras. It roughly follows the historical path of their discovery, made jointly with A.Zelevinsky. Total positivity serves as the main motivation.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/755c80fc500d4cd9666f49a2f0c3323cef149f40

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Positivity and higher Teichm\"uller theory (2018, methodology): “t real semisimple reductive Lie groups. It plays an important role in representation theory with many interesting relations to other areas in mathematics as well as to problems in theoretical physics [18, 1, 36]. A more algebro-geometric approach to Lusztig’s total positivity has been developed by F”
Cluster algebras and representation theory (2010, background): “A nice introduction [14] to these ideas is given in these proceedings, with many references to the growing literature on the subject.”
Ordered Exchange Graphs (2013, background): “More detailed surveys on some of the objects and maps include [105, 63, 31, 78, 90, 66].”
Cluster algebras and derived categories (2012, background): “Fomin and Zelevinsky’s main aim was to set up a combinatorial framework for the study of the so-called canonical bases which these algebras possess [78] [97] and which are closely related to the notion of total positivity [98] [41] in the associated varieties.”
Cluster algebras (2014, unknown): “Cluster algebras are a remarkable class of commutative rings introduced by Fomin and Zelevinsky [18,20] , see also [19] .”
Introduction to Cluster Algebras. Chapters 1-3 (2016, unknown): “Additional details and references can be found in [18].”
Cluster Algebras and Triangulated Surfaces Part II: Lambda Lengths (2012, background): “In particular, we do not cite the papers referencing this work, except for mentioning a very brief and informal survey [18].”
Cluster categories (2010, methodology): “We refer to the survey papers ([19],[45],[80],[81],[82],[83],[91],[99],[100],[104], [112]) for additional information.”