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Communications in Algebra Volume 24, 1996 - Issue 13
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Original Articles

On generalizations of root systems

Vera Serganova Dept. Of mathematics, University of california at berkeley, Berkeley, CA, 94720 E-mail: [email protected]
Pages 4281-4299 | Received 01 Jun 1996, Published online: 27 Jun 2007

Citations (37)

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Malihe Yousofzadeh. (2017) Locally finite root supersystems. Communications in Algebra 45:10, pages 4292-4320.
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V. Schreiber & A.P. Veselov. (2014) On deformation and classification of ∨-systems. Journal of Nonlinear Mathematical Physics 21:4, pages 543-583.
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DANIL CHAPOVALOV, MAXIM CHAPOVALOV, ALEXEI LEBEDEV & DIMITRY LEITES. (2010) THE CLASSIFICATION OF ALMOST AFFINE (HYPERBOLIC) LIE SUPERALGEBRAS. Journal of Nonlinear Mathematical Physics 17:sup1, pages 103-161.
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Articles from other publishers (34)

Andrey O Krutov, Réamonn Ó Buachalla & Karen R Strung. (2023) Nichols Algebras and Quantum Principal Bundles. International Mathematics Research Notices 2023:23, pages 20076-20117.
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Francesco Aprile & Paul Heslop. (2023) Superconformal Blocks in Diverse Dimensions and BC Symmetric Functions. Communications in Mathematical Physics 402:2, pages 995-1101.
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Alexander Sherman. (2023) Ghost Distributions on Supersymmetric Spaces II: Basic Classical Superalgebras. International Mathematics Research Notices.
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Maria Gorelik & Thorsten Heidersdorf. (2023) Gruson–Serganova character formulas and the Duflo–Serganova cohomology functor. Journal für die reine und angewandte Mathematik (Crelles Journal) 0:0.
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Malihe Yousofzadeh. (2022) Classification of bases of twisted affine root supersystems. Journal of Algebraic Combinatorics 55:3, pages 919-978.
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Alexander Sherman. (2022) Spherical supervarieties. Annales de l'Institut Fourier 71:4, pages 1449-1492.
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Ivan Dimitrov & Rita Fioresi. (2021) On Kostant root systems of Lie superalgebras. Journal of Algebra 570, pages 678-701.
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Abbas Darehgazani, Fateme Shirnejad & Malihe Yousofzadeh. (2021) Affine Lie superalgebras. Journal of Algebra 570, pages 636-677.
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Richard Stedman & Ian A. B. Strachan. (2021) Extended ⋁-systems and trigonometric solutions to the WDVV equations. Journal of Mathematical Physics 62:2.
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Alexander Sherman. (2020) Spherical indecomposable representations of Lie superalgebras. Journal of Algebra 547, pages 262-311.
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Sofiane Bouarroudj, Dimitry Leites, Olexander Lozhechnyk & Jin Shang. (2020) The Roots of Exceptional Modular Lie Superalgebras with Cartan Matrix. Arnold Mathematical Journal 6:1, pages 63-118.
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Dimitry Leites & Oleksandr Lozhechnyk. (2019) Inverses of Cartan matrices of Lie algebras and Lie superalgebras. Linear Algebra and its Applications 583, pages 195-256.
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Fateme Shirnejad & Malihe Yousofzadeh. (2019) Extended affine root supersystems of type A(ℓ,ℓ). Journal of Algebra 540, pages 42-62.
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A. N. Sergeev. (2018) Lie Superalgebras and Calogero–Moser–Sutherland Systems. Journal of Mathematical Sciences 235:6, pages 756-787.
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Iván Angiono & Hiroyuki Yamane. (2018) Bruhat order and nil-Hecke algebras for Weyl groupoids. Journal of Algebra and Its Applications 17:09, pages 1850166.
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Maria Gorelik & Ary Shaviv. (2017) Generalized reflection root systems. Journal of Algebra 491, pages 490-516.
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Nicolás Andruskiewitsch & Iván Angiono. (2017) On finite dimensional Nichols algebras of diagonal type. Bulletin of Mathematical Sciences 7:3, pages 353-573.
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Vera Serganova. 2017. Perspectives in Lie Theory. Perspectives in Lie Theory 125 177 .
Alexander N. Sergeev & Alexander P. Veselov. (2016) Orbits and Invariants of Super Weyl Groupoid. International Mathematics Research Notices, pages rnw182.
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V G Kac & M Wakimoto. (2016) Representations of affine superalgebras and mock theta functions. III. Izvestiya: Mathematics 80:4, pages 693-750.
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M. Yousofzadeh. (2016) Extended affine root supersystems. Journal of Algebra 449, pages 539-564.
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IVÁN ANGIONO. (2015) DISTINGUISHED PRE-NICHOLS ALGEBRAS. Transformation Groups 21:1, pages 1-33.
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Виктор Гершевич Кац, Victor Gershevich Kac, Minoru Wakimoto & Minoru Wakimoto. (2016) Representations of affine superalgebras and mock theta functions. IIIRepresentations of affine superalgebras and mock theta functions. III. Известия Российской академии наук. Серия математическая Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya 80:4, pages 65-122.
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Maria Gorelik & Victor G. Kac. (2015) Characters of (relatively) integrable modules over affine Lie superalgebras. Japanese Journal of Mathematics 10:2, pages 135-235.
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Alexander Alldridge & Sebastian Schmittner. (2015) Spherical representations of Lie supergroups. Journal of Functional Analysis 268:6, pages 1403-1453.
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Irfan Bagci & Samuel Chamberlin. (2014) Integral bases for the universal enveloping algebras of map superalgebras. Journal of Pure and Applied Algebra 218:8, pages 1563-1576.
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Alexander Sergeev & Alexander Veselov. (2011) Grothendieck rings of basic classical Lie superalgebras. Annals of Mathematics 173:2, pages 663-703.
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R. Fioresi & F. Gavarini. 2011. Supersymmetry in Mathematics and Physics. Supersymmetry in Mathematics and Physics 101 123 .
I. Heckenberger. (2010) Lusztig isomorphisms for Drinfel'd doubles of bosonizations of Nichols algebras of diagonal type. Journal of Algebra 323:8, pages 2130-2182.
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István Heckenberger & Hiroyuki Yamane. (2007) A generalization of Coxeter groups, root systems, and Matsumoto’s theorem. Mathematische Zeitschrift 259:2, pages 255-276.
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Nicolás Andruskiewitsch & Iván Ezequiel Angiono. 2008. Modules and Comodules. Modules and Comodules 47 64 .
S. Bouarroudj & D. Leites. (2007) Simple Lie superalgebras and nonintegrable distributions in characteristic p. Journal of Mathematical Sciences 141:4, pages 1390-1398.
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Gizem Karaali. (2004) Constructing r-matrices on simple Lie superalgebras. Journal of Algebra 282:1, pages 83-102.
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Pavel Grozman, Dimitry Leites & Irina Shchepochkina. 2003. The Orbit Method in Geometry and Physics. The Orbit Method in Geometry and Physics 101 146 .

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