Classification of Finite Dimensional Modular Lie Superalgebras with Indecomposable Cartan Matrix [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2009 Finite dimensional modular Lie superalgebras over algebraically closed fields with indecomposable Cartan matrices are classified under some technical, most probably inessential, hypotheses.
Sofiane Bouarroudj +2 more
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The (q, t)-Cartan matrix specialized at $$q=1$$ q = 1 and its applications [PDF]
Mathematische Zeitschrift, 2022 The ( q , t )-Cartan matrix specialized at $$t=1$$ t = 1 , usually called the quantum Cartan matrix , has deep connections with (i) the representation theory of its untwisted quantum affine algebra, and (ii) quantum unipotent coordinate algebra, root ...
M. Kashiwara, Se-jin Oh
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New Constructions of Exceptional Simple Lie Superalgebras with Integer Cartan Matrix in Characteristics 3 and 5 via Tensor Categories [PDF]
Transformation groups, 2021 Using tensor categories, we present new constructions of several of the exceptional simple Lie superalgebras with integer Cartan matrix in characteristic p = 3 and p = 5 from the complete classification of modular Lie superalgebras with indecomposable ...
Arun S. Kannan
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The Rank-One property for free Frobenius extensions
Comptes Rendus. Mathématique, 2023 A conjecture by the second author, proven by Bonnafé–Rouquier, says that the multiplicity matrix for baby Verma modules over the restricted rational Cherednik algebra has rank one over $\mathbb{Q}$ when restricted to each block of the algebra.In this ...
Bellamy, Gwyn, Thiel, Ulrich
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Cartan invariant matrices for finite monoids [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 Let $M$ be a finite monoid. In this paper we describe how the Cartan invariant matrix of the monoid algebra of $M$ over a field $\mathbb{K}$ of characteristic zero can be expressed using characters and some simple combinatorial statistic.
Nicolas M. Thiéry
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Cluster Structures on Double Bott–Samelson Cells
Forum of Mathematics, Sigma, 2021 Let $\mathsf {C}$ be a symmetrisable generalised Cartan matrix. We introduce four different versions of double Bott–Samelson cells for every pair of positive braids in the generalised braid group associated to $\mathsf {C}$ .
Linhui Shen, Daping Weng
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On the Higher Nash Blow-Up Derivation Lie Algebras of Isolated Hypersurface Singularities
Mathematics, 2023 It is a natural question to ask whether there is any Lie algebra that completely characterize simple singularities? The higher Nash blow-up derivation Lie algebras Lkl(V) associated to isolated hypersurface singularities defined to be the Lie algebra of ...
Muhammad Asif +3 more
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Projective class ring of a restricted quantum group $ \overline{U}_{q}(\mathfrak{sl}^{*}_2) $
AIMS Mathematics, 2023 In this paper, we compute the projective class ring of the new type restricted quantum group $ \overline{U}_{q}(\mathfrak{sl}^{*}_2) $. First, we describe the principal indecomposable projective $ \overline{U}_{q}(\mathfrak{sl}^{*}_2) $-modules and study
Pengcheng Ji, Jialei Chen, Fengxia Gao
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The Roots of Exceptional Modular Lie Superalgebras with Cartan Matrix [PDF]
Arnold Mathematical Journal, 2019 For each of the exceptional (not entering infinite series) finite-dimensional modular Lie superalgebras with indecomposable Cartan matrix, we give the explicit list of its roots, and the corresponding Chevalley basis, for one of its inequivalent Cartan ...
S. Bouarroudj +3 more
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Cokernels of the Cartan matrix and stratifying systems [PDF]
Communications in Algebra, 2018 We study the cokernel of the application given by the Cartan matrix CΛ of a finite dimensional k-algebra This produces a finitely generated abelian group, the Cartan group which is invariant under derived equivalences.
E. Marcos, O. Mendoza, C. S'aenz
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