R. Sherman, A. V. Zelevinskii, “Positivity and canonical bases in rank 2 cluster algebras of finite and affine types”, Mosc. Math. J., 4:4 (2004), 947

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Mosc. Math. J., 2004, том 4, номер 4, страницы 947–974 (Mi mmj178)

Эта публикация цитируется в 58 научных статьях (всего в 58 статьях)

Positivity and canonical bases in rank 2 cluster algebras of finite and affine types

[Положительность и канонические базисы в кластерных алгебрах ранга 2 конечного и аффинного типов]

P. Sherman, A. V. Zelevinskii

Northeastern University

Аннотация: Изучение кластерных алгебр было мотивировано желанием создать алгебраический формализм для понимания полной положительности и канонических базисов в полупростых алгебраических группах. В этой работе мы определяем и вычисляем канонический базис для специального семейства кластерных алгебр ранга 2.

DOI: https://doi.org/10.17323/1609-4514-2004-4-4-947-974

Полный текст: http://www.ams.org/.../abst4-4-2004.html

Список литературы: PDF файл HTML файл

Реферативные базы данных:

MSC: Primary 16S99; Secondary 05E15, 22E46
Статья поступила: 9 июля 2003 г.; исправленный вариант 14 декабря 2003 г.
Язык публикации: английский

Образец цитирования: R. Sherman, A. V. Zelevinskii, “Positivity and canonical bases in rank 2 cluster algebras of finite and affine types”, Mosc. Math. J., 4:4 (2004), 947–974

Цитирование в формате AMSBIB

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\paper Positivity and canonical bases in rank~2 cluster algebras of finite and affine types

\jour Mosc. Math.~J.

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\vol 4

\issue 4

\pages 947--974

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Образцы ссылок на эту страницу:

http://mi.mathnet.ru/mmj178

http://mi.mathnet.ru/rus/mmj/v4/i4/p947

ОТПРАВИТЬ:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

Эта публикация цитируется в следующих статьяx:

Berenstein A., Zelevinsky A., “Quantum cluster algebras”, Adv Math, 195:2 (2005), 405–455
Ph. Caldero, A. V. Zelevinskii, “Laurent expansions in cluster algebras via quiver representations”, Mosc. Math. J., 6:3 (2006), 411–429
Caldero Ph., Keller B., “From triangulated categories to cluster algebras. II”, Ann. Sci. Йcole Norm. Sup. (4), 39:6 (2006), 983–1009
Zhu Bin, “Applications of BGP-reflection functors: isomorphisms of cluster algebras”, Sci. China Ser. A, 49:12 (2006), 1839–1854
Buan A.B., Marsh R., “Cluster-tilting theory”, Trends in Representation Theory of Algebras and Related Topics, Contemporary Mathematics Series, 406, 2006, 1–30
Hasselblatt B., Propp J., “Degree-growth of monomial maps”, Ergodic Theory Dynam. Systems, 27:5 (2007), 1375–1397
Hone A.N.W., “Singularity confinement for maps with the Laurent property”, Phys. Lett. A, 361:4-5 (2007), 341–345
Fomin S., Zelevinsky A., “Cluster algebras. IV. Coefficients”, Compos. Math., 143:1 (2007), 112–164
Zelevinsky A., “Semicanonical basis generators of the cluster algebra of type $A_1^{(1)}$”, Electron. J. Combin., 14:1 (2007), N4, 5 pp.
Musiker G., Propp J., “Combinatorial interpretations for rank-two cluster algebras of affine type”, Electron. J. Combin., 14:1 (2007), R15, 23 pp.
Fock V.V., Goncharov A.B., “Cluster ensembles, quantization and the dilogarithm”, Ann. Sci. Éc. Norm. Supér. (4), 42:6 (2009), 865–930
Di Francesco Ph., Kedem R., “Positivity of the $T$-system cluster algebra”, Electron. J. Combin., 16:1 (2009), R140, 39 pp.
Schiffler R., Thomas H., “On cluster algebras arising from unpunctured surfaces”, Int. Math. Res. Not. IMRN, 2009, no. 17, 3160–3189
Dupont G., “Positivity in coefficient-free rank two cluster algebras”, Electron. J. Combin., 16:1 (2009), R98, 11 pp.
Philippe Di Francesco, Rinat Kedem, “$Q$-system Cluster Algebras, Paths and Total Positivity”, SIGMA, 6 (2010), 014, 36 pp.
Dupont G., “Quantized Chebyshev polynomials and cluster characters with coefficients”, J. Algebraic Combinatorics, 31:4 (2010), 501–532
Buan A.B., Marsh R.J., “Denominators in cluster algebras of affine type”, J. Algebra, 323:8 (2010), 2083–2102
Schiffler R., “On cluster algebras arising from unpunctured surfaces. II”, Adv. Math., 223:6 (2010), 1885–1923
Di Francesco Ph., Kedem R., “Discrete Non-commutative Integrability: Proof of a Conjecture by M. Kontsevich”, Int Math Res Not, 2010, no. 21, 4042–4063
Assem I., Reutenauer Ch., Smith D., “Friezes”, Adv Math, 225:6 (2010), 3134–3165
Dupont G., “Transverse quiver Grassmannians and bases in affine cluster algebras”, Algebra & Number Theory, 4:5 (2010), 599–624
Musiker G., Schiffler R., “Cluster expansion formulas and perfect matchings”, J Algebraic Combin, 32:2 (2010), 187–209
Nakajima H., “Quiver varieties and cluster algebras”, Kyoto Journal of Mathematics, 51:1 (2011), 71–126
Dupont G., “Generic variables in acyclic cluster algebras”, J Pure Appl Algebra, 215:4 (2011), 628–641
Keller B., “Cluster Algebras and Cluster Categories”, Bulletin of the Iranian Mathematical Society, 37:2 (2011), 187–234
Chen X., Ding M., Sheng J., “Bar-invariant bases of the quantum cluster algebra of type A (2) ((2))”, Czechoslovak Math J, 61:4 (2011), 1077–1090
Plamondon P.-G., “Cluster algebras via cluster categories with infinite-dimensional morphism spaces”, Compos Math, 147:6 (2011), 1921–1954
Di Francesco Ph., Kedem R., “Non-commutative integrability, paths and quasi-determinants”, Adv Math, 228:1 (2011), 97–152
Lampe Ph., “A Quantum Cluster Algebra of Kronecker Type and the Dual Canonical Basis”, Int Math Res Not, 2011, no. 13, 2970–3005
Musiker G., “A Graph Theoretic Expansion Formula for Cluster Algebras of Classical Type”, Ann Comb, 15:1 (2011), 147–184
Musiker G., Schiffler R., Williams L., “Positivity for cluster algebras from surfaces”, Adv Math, 227:6 (2011), 2241–2308
Keller B., “Accumulated Algebra and Applications”, Asterisque, 2011, no. 339, 63–90
Irelli G.C. Esposito F., “Geometry of Quiver Grassmannians of Kronecker Type and Applications to Cluster Algebras”, Algebr. Number Theory, 5:6 (2011), 777–801
Dupont G., “Generic Cluster Characters”, Int Math Res Not, 2012, no. 2, 360–393
Assem I., Dupont G., Schiffler R., Smith D., “Friezes, Strings and Cluster Variables”, Glasg Math J, 54:1 (2012), 27–60
Ding M. Xu F., “A Z-Basis for the Cluster Algebra of Type (D)Over-Tilde(4)”, Algebr. Colloq., 19:4 (2012), 591–610
Irelli G.C., “Cluster Algebras of Type a(2)((1))”, Algebr. Represent. Theory, 15:5 (2012), 977–1021
Ding Ming X.F., “A Quantum Analogue of Generic Bases for Affine Cluster Algebras”, Sci. China-Math., 55:10 (2012), 2045–2066
Dupont G., “Positivity for Regular Cluster Characters in Acyclic Cluster Algebras”, J. Algebra. Appl., 11:4 (2012), 1250069
Lee K., “On Cluster Variables of Rank Two Acyclic Cluster Algebras”, Ann. Comb., 16:2 (2012), 305–317
Ding M. Xu F., “Bases of the Quantum Cluster Algebra of the Kronecker Quiver”, Acta. Math. Sin.-English Ser., 28:6 (2012), 1169–1178
Keller B., “Cluster Algebras and Derived Categories”, Derived Categories in Algebraic Geometry - Tokyo 2011, EMS Ser. Congr. Rep., ed. Kawamata Y., Eur. Math. Soc., 2012, 123–183
Ding M. Xiao J. Xu F., “Integral Bases of Cluster Algebras and Representations of Tame Quivers”, Algebr. Represent. Theory, 16:2 (2013), 491–525
Lee K. Schiffler R., “A Combinatorial Formula for Rank 2 Cluster Variables”, J. Algebr. Comb., 37:1 (2013), 67–85
Lee K., Li L., Zelevinsky A., “Positivity and Tameness in Rank 2 Cluster Algebras”, J. Algebr. Comb., 40:3 (2014), 823–840
Lee K., Li L., Rupel D., Zelevinsky A., “Greedy Bases in Rank 2 Quantum Cluster Algebras”, Proc. Natl. Acad. Sci. U. S. A., 111:27 (2014), 9712–9716
Shen L., “Stasheff Polytopes and the Coordinate Ring of the Cluster X-Variety of Type a(N)”, Sel. Math.-New Ser., 20:3 (2014), 929–959
Lee K., Li L., Zelevinsky A., “Greedy Elements in Rank 2 Cluster Algebras”, Sel. Math.-New Ser., 20:1 (2014), 57–82
Emily Gunawan, Gregg Musiker, “$T$-Path Formula and Atomic Bases for Cluster Algebras of Type $D$”, SIGMA, 11 (2015), 060, 46 pp.
Lee K., Schiffler R., “Positivity For Cluster Algebras”, Ann. Math., 182:1 (2015), 73–125
Blanc J., Dolgachev I., “Automorphisms of Cluster Algebras of Rank 2”, Transform. Groups, 20:1 (2015), 1–20
Chen X. Ding M. Xu F., “Positivity For Generalized Cluster Variables of Affine Quivers”, Algebr. Represent. Theory, 19:6 (2016), 1495–1506
Fraser Ch., “Quasi-Homomorphisms of Cluster Algebras”, Adv. Appl. Math., 81 (2016), 40–77
Lee K., Li L., Rupel D., Zelevinsky A., “the Existence of Greedy Bases in Rank 2 Quantum Cluster Algebras”, Adv. Math., 300 (2016), 360–389
Fomin S. Pylyayskyy P., “Tensor Diagrams and Cluster Algebras”, Adv. Math., 300 (2016), 717–787
Muller G., “Skein and Cluster Algebras of Marked Surfaces”, Quantum Topol., 7:3 (2016), 435–503
Cheung M.W., Gross M., Muller G., Musiker G., Rupel D., Stella S., Williams H., “the Greedy Basis Equals the Theta Basis: a Rank Two Haiku”, J. Comb. Theory Ser. A, 145 (2017), 150–171
Felikson A., Tumarkin P., “Bases For Cluster Algebras From Orbifolds”, Adv. Math., 318 (2017), 191–232

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