Results 1 to 10 of about 382 (159)
Cokernels of the Cartan matrix and stratifying systems [PDF]
Communications in Algebra, 2019 We study the cokernel of the application given by the Cartan Matrix $C_Λ$ of a finite dimensional $k$-algebra $Λ.$ This produces a finitely generated abelian group, the Cartan group $G_Λ,$ which is invariant under derived equivalences. We are interested in the case when $G_Λ$ is finite.
Octavio Mendoza, Corina Saenz
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The Roots of Exceptional Modular Lie Superalgebras with Cartan Matrix [PDF]
Arnold Mathematical Journal, 2020 For each of the exceptional Lie superalgebras with indecomposable Cartan matrix, we give the explicit list of its roots of and the corresponding Chevalley basis for one of the inequivalent Cartan matrices, the one corresponding to the greatest number of mutually orthogonal isotropic odd simple roots.
Jin Shang +2 more
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The Cartan matrix of a centralizer algebra
Proceedings of the Indian Academy of Sciences: Mathematical Sciences, 2012 The centralizer algebra of a matrix consists of those matrices that commute with it. We investigate the basic representation-theoretic invariants of centralizer algebras, namely their radicals, projective indecomposable modules, injective indecomposable modules, simple modules and Cartan matrices.
Pooja Singla +2 more
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The Cartan matrix and enumerative calculus
Journal of Symbolic Computation, 2004 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xuezhi Zhao, Haibao Duan
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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 spectral radius of the Coxeter transformations for a generalized Cartan matrix [PDF]
Mathematische Annalen, 1994 This work concerns the eigenvalues (more precisely, the spectral radius) of the Coxeter transformations \(C = C(A, \pi)\) for a generalized Cartan matrix \(A\) [for such matrices see \textit{V. Kac} ``Infinite dimensional Lie algebras'', 2nd ed. Cambridge Univ. Press (1985; Zbl 0574.17010); 3rd ed. (1990; Zbl 0716.17022)].
Claus Michael Ringel +1 more
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The Cartan matrix of the Schur algebra S(2, r)
Archiv Der Mathematik, 2001 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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