Using the connection between McKay quiver and Loewy matrix, and the properties of characteristic polynomial of Loewy matrix, we give a generalized way to determine the McKay quiver for a finite subgroup of a generaliz...Using the connection between McKay quiver and Loewy matrix, and the properties of characteristic polynomial of Loewy matrix, we give a generalized way to determine the McKay quiver for a finite subgroup of a generalized linear group.展开更多
Let H be a finite-dimensional pointed rank one Hopf algebra of nilpotent type over a finite group G.In this paper,we investigate the McKay matrix WV of H for tensoring with the 2-dimensional indecomposable H-module V:...Let H be a finite-dimensional pointed rank one Hopf algebra of nilpotent type over a finite group G.In this paper,we investigate the McKay matrix WV of H for tensoring with the 2-dimensional indecomposable H-module V:=M(2,0).It turns out that the characteristic polynomial,eigenvalues and eigenvectors of WV are related to the character table of the finite group G and a kind of generalized Fibonacci polynomial.Moreover,we construct some eigenvectors of each eigenvalue for WV by using the factorization of the generalized Fibonacci polynomial.As an example,we explicitly compute the characteristic polynomial and eigenvalues of WV and give all eigenvectors of each eigenvalue for WV when G is a dihedral group of order 4N+2.展开更多
For each finite subgroup G of SLn（C）, we introduce the generalized Cartan matrix AG in view of McKay correspondence from the fusion rule of its natural representation. Using group theory, we show that the generalize...For each finite subgroup G of SLn（C）, we introduce the generalized Cartan matrix AG in view of McKay correspondence from the fusion rule of its natural representation. Using group theory, we show that the generalized Cartan matrices have similar favorable properties such as positive semi- definiteness as in the classical case of affine Cartan matrices. The complete McKay quivers for SL3 （C） are explicitly described and classified based on representation theory.展开更多
In this paper, we prove that the McKay conjecture holds for finite groups with abelian Sylow 3-subgroups and any prime l via the inductive McKay condition.2010 Mathematics Subject Classification： 20C15, 20C33
In this paper, we introduce the m-Cartan matrix and observe that some properties of the quadratic form associated to the Cartan matrix of an Euclidean diagram can be generalized to the m-Cartan matrix of a McKay quive...In this paper, we introduce the m-Cartan matrix and observe that some properties of the quadratic form associated to the Cartan matrix of an Euclidean diagram can be generalized to the m-Cartan matrix of a McKay quiver. We also describe the McKay quiver for a finite abelian subgroup of a special linear group.展开更多
In this paper,we show that the McKay quiver of a finite subgroup of a general linear group is a regular covering of the McKay quiver of its intersection with the special linear group.Using this and our results on &quo...In this paper,we show that the McKay quiver of a finite subgroup of a general linear group is a regular covering of the McKay quiver of its intersection with the special linear group.Using this and our results on "returning arrows" in McKay quiver,we give an algorithm to construct the McKay quiver of a finite abelian group.Using this construction,we show how the cone and cylinder of an(n-1)-Auslander absolute n-complete algebra are truncated from the McKay quivers of abelian groups.展开更多
基金Foundation item:This work is partly supported by NSF(103710036)of Chinakey project(02A024)of provincial Ministry of Foundation of Hunan.
文摘Using the connection between McKay quiver and Loewy matrix, and the properties of characteristic polynomial of Loewy matrix, we give a generalized way to determine the McKay quiver for a finite subgroup of a generalized linear group.
文摘Let H be a finite-dimensional pointed rank one Hopf algebra of nilpotent type over a finite group G.In this paper,we investigate the McKay matrix WV of H for tensoring with the 2-dimensional indecomposable H-module V:=M(2,0).It turns out that the characteristic polynomial,eigenvalues and eigenvectors of WV are related to the character table of the finite group G and a kind of generalized Fibonacci polynomial.Moreover,we construct some eigenvectors of each eigenvalue for WV by using the factorization of the generalized Fibonacci polynomial.As an example,we explicitly compute the characteristic polynomial and eigenvalues of WV and give all eigenvectors of each eigenvalue for WV when G is a dihedral group of order 4N+2.
基金supported by National Natural Science Foundation of China (Grant No. 10728102)National Security Agency (Grant No. MDA 904-97-1-0062)
文摘For each finite subgroup G of SLn（C）, we introduce the generalized Cartan matrix AG in view of McKay correspondence from the fusion rule of its natural representation. Using group theory, we show that the generalized Cartan matrices have similar favorable properties such as positive semi- definiteness as in the classical case of affine Cartan matrices. The complete McKay quivers for SL3 （C） are explicitly described and classified based on representation theory.
文摘In this paper, we prove that the McKay conjecture holds for finite groups with abelian Sylow 3-subgroups and any prime l via the inductive McKay condition.2010 Mathematics Subject Classification： 20C15, 20C33
基金supported by National Natural Science Foundation of China (Grant No. 10671061)theResearch Foundation for Doctor Programme (Grant No. 200505042004)
文摘In this paper, we introduce the m-Cartan matrix and observe that some properties of the quadratic form associated to the Cartan matrix of an Euclidean diagram can be generalized to the m-Cartan matrix of a McKay quiver. We also describe the McKay quiver for a finite abelian subgroup of a special linear group.
基金supported by National Natural Science Foundation of China (Grant No.10971172)
文摘In this paper,we show that the McKay quiver of a finite subgroup of a general linear group is a regular covering of the McKay quiver of its intersection with the special linear group.Using this and our results on "returning arrows" in McKay quiver,we give an algorithm to construct the McKay quiver of a finite abelian group.Using this construction,we show how the cone and cylinder of an(n-1)-Auslander absolute n-complete algebra are truncated from the McKay quivers of abelian groups.
