Within the framework of continuum model,we study the projective representation of emergent D_(6)point group in twisted bilayer graphene.We then construct tight-binding models of the lowest bands without and with exter...Within the framework of continuum model,we study the projective representation of emergent D_(6)point group in twisted bilayer graphene.We then construct tight-binding models of the lowest bands without and with external electromagnetic fields,based on the projective representation.展开更多
This is a contribution to the project of quiver approaches to quasi-quantum groups.We classify Majid bimodules over groups with 3-cocycles by virtue of projective representations.This leads to a theoretic classificati...This is a contribution to the project of quiver approaches to quasi-quantum groups.We classify Majid bimodules over groups with 3-cocycles by virtue of projective representations.This leads to a theoretic classification of graded pointed Majid algebras over path coalgebras,or equivalently cofree pointed coalgebras,and helps to provide a projective representation-theoretic description of the gauge equivalence of graded pointed Majid algebras.We apply this machinery to construct some concrete examples and obtain a classification of finite-dimensional graded pointed Majid algebras with the set of group-likes equal to the cyclic group of order 2.展开更多
We study inhomogeneous projective oscillator representations of Lie superalgebras of Qtype on supersymmetric polynomial algebras.These representations are infinite-dimensional.We prove that they are completely reducib...We study inhomogeneous projective oscillator representations of Lie superalgebras of Qtype on supersymmetric polynomial algebras.These representations are infinite-dimensional.We prove that they are completely reducible.Moreover,these modules are explicitly decomposed as direct sums of two irreducible submodules.展开更多
Operator-valued frames are natural generalization of frames that have been used in many applied areas such as quantum computing, packets encoding and sensor networks. We focus on developing the theory about operator-v...Operator-valued frames are natural generalization of frames that have been used in many applied areas such as quantum computing, packets encoding and sensor networks. We focus on developing the theory about operator-valued frame generators for projective unitary representations of finite or countable groups which can be viewed as the theory of quantum channels with group structures. We present new results for operator-valued frames concerning (general and structured) dilation property, orthogonal frames, frame representation and dual frames. Our results are complementary to some of the recent work of Kaftal, Larson and Zhang, and in some cases our treatment is more elementary and transparent.展开更多
Let г^＋ be the positive cone of a totally ordered abelian group г, and σa cocycle in г. We study the twisted crossed products by actions of г＋ as endomorphisms of C^＊-algebras, and use this to generalize the t...Let г^＋ be the positive cone of a totally ordered abelian group г, and σa cocycle in г. We study the twisted crossed products by actions of г＋ as endomorphisms of C^＊-algebras, and use this to generalize the theorem of Ji.展开更多
基金DOE Office of Basic Energy SciencesDivision of Materials Sciences and Engineering under Award DE-SC0010526。
文摘Within the framework of continuum model,we study the projective representation of emergent D_(6)point group in twisted bilayer graphene.We then construct tight-binding models of the lowest bands without and with external electromagnetic fields,based on the projective representation.
基金supported by National Natural Science Foundation of China(Grant No. 10601052)Natural Science Foundation of Shandong Province(Grant No.2009ZRA01128)the Independent Innovation Foundation of Shandong University(Grant No.2010TS021)
文摘This is a contribution to the project of quiver approaches to quasi-quantum groups.We classify Majid bimodules over groups with 3-cocycles by virtue of projective representations.This leads to a theoretic classification of graded pointed Majid algebras over path coalgebras,or equivalently cofree pointed coalgebras,and helps to provide a projective representation-theoretic description of the gauge equivalence of graded pointed Majid algebras.We apply this machinery to construct some concrete examples and obtain a classification of finite-dimensional graded pointed Majid algebras with the set of group-likes equal to the cyclic group of order 2.
基金Supported by the Fundamental Research Funds for the Central Universities。
文摘We study inhomogeneous projective oscillator representations of Lie superalgebras of Qtype on supersymmetric polynomial algebras.These representations are infinite-dimensional.We prove that they are completely reducible.Moreover,these modules are explicitly decomposed as direct sums of two irreducible submodules.
基金supported by Singapore Ministry of Education Academic Research Fund Tier 1 (Grant No. R-146-000-136-112)National Natural Science Foundation of China (Grant No. 10771101)US National Science Foundation (Grant No. DMS-1106934)
文摘Operator-valued frames are natural generalization of frames that have been used in many applied areas such as quantum computing, packets encoding and sensor networks. We focus on developing the theory about operator-valued frame generators for projective unitary representations of finite or countable groups which can be viewed as the theory of quantum channels with group structures. We present new results for operator-valued frames concerning (general and structured) dilation property, orthogonal frames, frame representation and dual frames. Our results are complementary to some of the recent work of Kaftal, Larson and Zhang, and in some cases our treatment is more elementary and transparent.
基金the Academy of Sciences of Malaysia through SAGA Projectthe Indonesian Research Fund for Doctorate Sandwich Programs(URGE)
文摘Let г^＋ be the positive cone of a totally ordered abelian group г, and σa cocycle in г. We study the twisted crossed products by actions of г＋ as endomorphisms of C^＊-algebras, and use this to generalize the theorem of Ji.
