基于某一未定型广义Cartan矩阵的fusion环的构造
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摘要
利用fusion环的一些性质,基于给定的未定型广义Cartan矩阵,构造了两类fusion环.结果表明这两类fusion环均为类群fusion环.
Based on some properties of fusion ring,two types of fusion rings are constructed from a given generalized Cartan matrix of indefinite type.It turns out that the two fusion rings are both near-group rings.
Based on some properties of fusion ring,two types of fusion rings are constructed from a given generalized Cartan matrix of indefinite type.It turns out that the two fusion rings are both near-group rings.
引文
[1]Moore G,Seiberg N.Classical and quantum conformal field theory[J].Comm Math Phys,1989,123:177-254.
[2]Francesco P,Mathieu P,Senechal D.Conformal field theory[M].New York Springer-Verlag,1997.
[3]Bakalov B,Kirillov A A.Lectures on tensor categories and modular functors[M].Providence Amer Math Soc,2001.
[4]Gepner D,Kapustin A.On the classification of fusion rings[J].Physics Letters B,1995,349:71-75.
[5]Larson H K.Pseudo-unitary non-selfdual fusion categories of ran k 4[J].J Algebra,2014,415:184-213.
[6]Ostrik V.Pivotal fusion categories of rank 3[J].Moscow Math J,2015,15:373-396.
[7]OstrikV.On formal codegrees of fusion categories[J].Math Res Lett,2009,16:.895-901.
[8]Kac V G.Infinite dimensional Lie Algebras[M].Cambridge Cambridge University Press,1990.
[9]Zhihua Wang,Libin Li.On realization of fusion rings from generalized Caxtan matrices[J].Acta Math Sinica,2017,33(3):362-376.
[10]Ostrik V..Fusion categories of rank 2[J].Math Res Lett,2003,10:177-184.
[11]Siehler J.Near-group categories[J].Alg Geom Topol,2003,3:719-775.
[12]Lorenz M.Some applications of Frobenius algebras to Hopf algebras[J].Gontemp Math,2011,537:269-289.
[2]Francesco P,Mathieu P,Senechal D.Conformal field theory[M].New York Springer-Verlag,1997.
[3]Bakalov B,Kirillov A A.Lectures on tensor categories and modular functors[M].Providence Amer Math Soc,2001.
[4]Gepner D,Kapustin A.On the classification of fusion rings[J].Physics Letters B,1995,349:71-75.
[5]Larson H K.Pseudo-unitary non-selfdual fusion categories of ran k 4[J].J Algebra,2014,415:184-213.
[6]Ostrik V.Pivotal fusion categories of rank 3[J].Moscow Math J,2015,15:373-396.
[7]OstrikV.On formal codegrees of fusion categories[J].Math Res Lett,2009,16:.895-901.
[8]Kac V G.Infinite dimensional Lie Algebras[M].Cambridge Cambridge University Press,1990.
[9]Zhihua Wang,Libin Li.On realization of fusion rings from generalized Caxtan matrices[J].Acta Math Sinica,2017,33(3):362-376.
[10]Ostrik V..Fusion categories of rank 2[J].Math Res Lett,2003,10:177-184.
[11]Siehler J.Near-group categories[J].Alg Geom Topol,2003,3:719-775.
[12]Lorenz M.Some applications of Frobenius algebras to Hopf algebras[J].Gontemp Math,2011,537:269-289.