scholarly journals Cartan matrices and Brauerʼs k(B)-conjecture II

2011 ◽  
Vol 337 (1) ◽  
pp. 345-362 ◽  
Author(s):  
Benjamin Sambale
Keyword(s):  
Cartan Matrices

Homological Aspects of Semigroup Gradings on Rings and Algebras

1999 ◽  
Vol 51 (3) ◽  
pp. 488-505 ◽  
Author(s):  
W. D. Burgess ◽  
Manuel Saorín
Keyword(s):  
Euler Characteristic ◽  
Division Ring ◽  
Artinian Ring ◽  
Global Dimension ◽  
Monomial Algebra ◽  
Finite Dimensional ◽  
Cartan Matrices ◽  
Torsion Free ◽  
Rings And Algebras ◽  
Finite Dimensional Algebras

AbstractThis article studies algebras R over a simple artinian ring A, presented by a quiver and relations and graded by a semigroup Σ. Suitable semigroups often arise from a presentation of R. Throughout, the algebras need not be finite dimensional. The graded K0, along with the Σ-graded Cartan endomorphisms and Cartan matrices, is examined. It is used to study homological properties.A test is found for finiteness of the global dimension of a monomial algebra in terms of the invertibility of the Hilbert Σ-series in the associated path incidence ring.The rationality of the Σ-Euler characteristic, the Hilbert Σ-series and the Poincaré-Betti Σ-series is studied when Σ is torsion-free commutative and A is a division ring. These results are then applied to the classical series. Finally, we find new finite dimensional algebras for which the strong no loops conjecture holds.

Root systems and inflations of non-negative quasi-Cartan matrices

2019 ◽  
Vol 580 ◽  
pp. 128-165 ◽  
Author(s):  
Bartosz Makuracki ◽  
Andrzej Mróz
Keyword(s):  
Root Systems ◽  
Cartan Matrices

Cartan matrices for restricted Lie algebras

2013 ◽  
Vol 275 (1-2) ◽  
pp. 569-594 ◽  
Author(s):  
Jens Carsten Jantzen
Keyword(s):  
Lie Algebras ◽  
Restricted Lie Algebras ◽  
Cartan Matrices

scholarly journals Quivers with relations for symmetrizable Cartan matrices IV: crystal graphs and semicanonical functions

2018 ◽  
Vol 24 (4) ◽  
pp. 3283-3348
Author(s):  
Christof Geiss ◽  
Bernard Leclerc ◽  
Jan Schröer
Keyword(s):  
Crystal Graphs ◽  
Cartan Matrices

scholarly journals Inverses of Cartan matrices of Lie algebras and Lie superalgebras

2019 ◽  
Vol 583 ◽  
pp. 195-256 ◽  
Author(s):  
Dimitry Leites ◽  
Oleksandr Lozhechnyk
Keyword(s):  
Lie Algebras ◽  
Lie Superalgebras ◽  
Cartan Matrices

scholarly journals Cartan matrices and integrable lattice Toda field equations

2011 ◽  
Vol 44 (46) ◽  
pp. 465202 ◽  
Author(s):  
Ismagil Habibullin ◽  
Kostyantyn Zheltukhin ◽  
Marina Yangubaeva
Keyword(s):  
Field Equations ◽  
Integrable Lattice ◽  
Cartan Matrices
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