Results 11 to 20 of about 2,177,540 (199)
On the Cartan matrix of Mackey algebras [PDF]
Transactions of the American Mathematical Society, 2009 Let k be a field of characteristic p>0, and G be a finite group. The first result of this paper is an explicit formula for the determinant of the Cartan matrix of the Mackey algebra mu_k(G) of G over k.
Bouc, Serge
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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.
H. Duan, Xuan Zhao, Xuezhi Zhao
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A new relation among Cartan matrix and Coxeter matrix
Journal of Algebra, 1987 The object of the paper is to show a relation between invariants of a root system R of type \(A_{\ell}\) (\(\ell odd)\), \(D_{\ell}, E_ 6, E_ 7\), or \(E_ 8\). On the one hand there are invariants p, q, r, and d associated to a Cartan matrix of R as follows.
Kyoji Saito
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On the Cartan matrix of an artin algebra of global dimension two
Journal of Algebra, 1983 The purpose of this paper is to show that if n is an artin algebra of g!obal dimension (81 dim) 2, then the determinant of its Cartan matrix equals + I. This generalizes previous results of Donovan and Freislich [2], Igusa and Todorov ]4 ] and Wilson [5]. We recall that if n is an artin algebra (for instance, a finite-dimensional algebra over a field),
D. Zacharia
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Quadratic algorithm to compute the Dynkin type of a positive definite quasi-Cartan matrix
Mathematics of Computation, 2020 Cartan matrices and quasi-Cartan matrices play an important role in such areas as Lie theory, representation theory, and algebraic graph theory. It is known that each (connected) positive definite quasi-Cartan matrix A ∈
Bartosz Makuracki, Andrzej Mróz
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Lax pairs for string Newton Cartan geometry
Nuclear Physics B, 2020 In this paper, based on a systematic formulation of Lax pairs, we show classical integrability for nonrelativistic strings propagating over stringy Newton-Cartan (NC) geometry.
Dibakar Roychowdhury
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Semiclassical dynamics for torsional Newton-Cartan strings
Nuclear Physics B, 2020 We explore folded spinning string configurations over torsional Newton Cartan (TNC) geometry with R×S2 topology within the semiclassical approximation. We consider the large c and/or nonrelativistic (NR) limit associated with the world-sheet d.o.f.
Dibakar Roychowdhury
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Cyclic homology and the determinant of the Cartan matrix
Journal of Pure and Applied Algebra, 1992 Let \(\Lambda = \bigoplus^ \infty_{i = 0} \Lambda_ i\) be a graded algebra over the field \(K\) and let \(R\) denote the ideal \(\bigoplus^ \infty_{i = 1} \Lambda_ i\). Each \(\Lambda_ i\) should be finite dimensional over \(K\), and \(D = \Lambda_ 0 = D_ 1 \times \cdots \times D_ m\) should be a product of finitely many finite-dimensional separable ...
Kiyoshi Igusa
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On the Cartan decomposition for classical random matrix ensembles
Journal of Mathematical Physics, 2022 We complete Dyson’s dream by cementing the links between symmetric spaces and classical random matrix ensembles. Previous work has focused on a one-to-one correspondence between symmetric spaces and many but not all of the classical random matrix ensembles. This work shows that we can completely capture all of the classical random matrix ensembles from
Alan Edelman, Sungwoo Jeong
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A new class of higher quantum Airy structures as modules of $\mathcal{W}(\mathfrak{gl}_r)$-algebras
SciPost Physics, 2023 Quantum $r$-Airy structures can be constructed as modules of $\mathcal{W}(\mathfrak{gl}_r)$-algebras via restriction of twisted modules for the underlying Heisenberg algebra.
Vincent Bouchard, Kieran Mastel
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