We classify condensable𝐸E_(2)-algebras in a modular tensor category C up to 2-Morita equivalence.Physically,this classification provides an explicit criterion to determine when distinct condensable𝐸E_(...We classify condensable𝐸E_(2)-algebras in a modular tensor category C up to 2-Morita equivalence.Physically,this classification provides an explicit criterion to determine when distinct condensable𝐸E_(2)-algebras yield the same condensed topological phase under a two-dimensional anyon condensation process.The relations between different condensable algebras can be translated into their module categories,interpreted physically as gapped domain walls in topological orders.As concrete examples,we interpret the categories of quantum doubles of finite groups and examples beyond group symmetries.Our framework fully elucidates the interplay among condensable𝐸E_(1)-algebras in C,condensable𝐸E_(2)-algebras in C up to 2-Morita equivalence,and Lagrangian algebras in C⊠C.展开更多
The concept of weak Hopf group coalgebras is a natural generalization of the notions of both weak Hopf algebras（quantum groupoids） and Hopf group coalgebras.Let π be a group.The Morita context is considered in the ...The concept of weak Hopf group coalgebras is a natural generalization of the notions of both weak Hopf algebras（quantum groupoids） and Hopf group coalgebras.Let π be a group.The Morita context is considered in the sense of weak Hopf π-coalgebras.Let H be a finite type weak Hopf π-coalgebra,and A a weak right π-H-comodule algebra.It is constructed that a Morita context connects A#H＊ which is a weak smash product and the ring of coinvariants AcoH.This result is the generalization of that of Wang＇s in the paper ＂Morita contexts,π-Galois extensions for Hopf π-coalgebras＂ in 2006.Furthermore,the result is important for constructing weak π-Galois extensions.展开更多
基金supported by Research Grants Council(RGC),University Grants Committee(UGC)of Hong Kong(ECS No.24304722)。
文摘We classify condensable𝐸E_(2)-algebras in a modular tensor category C up to 2-Morita equivalence.Physically,this classification provides an explicit criterion to determine when distinct condensable𝐸E_(2)-algebras yield the same condensed topological phase under a two-dimensional anyon condensation process.The relations between different condensable algebras can be translated into their module categories,interpreted physically as gapped domain walls in topological orders.As concrete examples,we interpret the categories of quantum doubles of finite groups and examples beyond group symmetries.Our framework fully elucidates the interplay among condensable𝐸E_(1)-algebras in C,condensable𝐸E_(2)-algebras in C up to 2-Morita equivalence,and Lagrangian algebras in C⊠C.
基金The Scientific Research Innovation Project for College Graduates in Jiangsu Province(No.CXLX_0094)
文摘The concept of weak Hopf group coalgebras is a natural generalization of the notions of both weak Hopf algebras（quantum groupoids） and Hopf group coalgebras.Let π be a group.The Morita context is considered in the sense of weak Hopf π-coalgebras.Let H be a finite type weak Hopf π-coalgebra,and A a weak right π-H-comodule algebra.It is constructed that a Morita context connects A#H＊ which is a weak smash product and the ring of coinvariants AcoH.This result is the generalization of that of Wang＇s in the paper ＂Morita contexts,π-Galois extensions for Hopf π-coalgebras＂ in 2006.Furthermore,the result is important for constructing weak π-Galois extensions.
