Quantum algorithms bring great challenges to classical public key cryptosystems, which makes cryptosystems based on non-commutative algebraic systems hop topic. The braid groups, which are non-commutative, have attrac...Quantum algorithms bring great challenges to classical public key cryptosystems, which makes cryptosystems based on non-commutative algebraic systems hop topic. The braid groups, which are non-commutative, have attracted much attention as a new platform for constructing quantum attack-resistant cryptosystems. A ring signature scheme is proposed based on the difficulty of the root extraction problem over braid groups, which can resist existential forgery against the adaptively cho-sen-message attack under the random oracle model.展开更多
Motivated by the work of Birman about the relationship between mapping class groups and braid groups,the authors discuss the relationship between the orbit braid group and the equivariant mapping class group on the cl...Motivated by the work of Birman about the relationship between mapping class groups and braid groups,the authors discuss the relationship between the orbit braid group and the equivariant mapping class group on the closed surface M with a free and proper group action in this paper.Their construction is based on the exact sequence given by the fibration F_(0)^(G) M→F(M/G,n).The conclusion is closely connected with the braid group of the quotient space.Comparing with the situation without the group action,there is a big difference when the quotient space is T^(2).展开更多
We unify and generalize several approaches to constructing braid group representa-tions from finite groups,using iterated twisted tensor products.We provide some general characterizations and classification of these r...We unify and generalize several approaches to constructing braid group representa-tions from finite groups,using iterated twisted tensor products.We provide some general characterizations and classification of these representations,focusing on the size of their images,which are typically finite groups.The well-studied Gaussian representations associated with metaplectic modular categories can be understood in this framework,and we give some new examples to illustrate their ubiquity.Our results suggest a relationship between the braiding on the G-gaugings of a pointed modular category C(A,Q)and that of C(A,Q)itself.展开更多
A series of irreducible representations of braid group Bn are given.By means of a generalized Conway relation (gi-q)(gi+p) = 0,a complete set of operators H(i) are constructed.With the eigenvectors of H(i) as represen...A series of irreducible representations of braid group Bn are given.By means of a generalized Conway relation (gi-q)(gi+p) = 0,a complete set of operators H(i) are constructed.With the eigenvectors of H(i) as representation bases,the biparametric irreducible representations of Bn are obtained by the help of Yang diagrams.展开更多
We survey various generalizations of braid groups for quivers with superpotential and focus on the cluster braid groups, which are introduced in a joint work with King (2018). Our motivations come from the study of cl...We survey various generalizations of braid groups for quivers with superpotential and focus on the cluster braid groups, which are introduced in a joint work with King (2018). Our motivations come from the study of cluster algebras, Calabi-Yau categories and Bridgeland stability conditions.展开更多
A unit cell geometrical structure was found with the use of symmetry operations corresponding to the point group C3. Based on the symmetry of space group R3, a 3D braided geometrical structure was obtained by transfor...A unit cell geometrical structure was found with the use of symmetry operations corresponding to the point group C3. Based on the symmetry of space group R3, a 3D braided geometrical structure was obtained by transforming the unit-cell. The features corresponding to this braided structure were studied. The fiber volume percentage and variational tendencies of the material were predicted by establishing a geometric model.展开更多
基金Supported by the National Natural Science Foundation of China (No. 10501053)
文摘Quantum algorithms bring great challenges to classical public key cryptosystems, which makes cryptosystems based on non-commutative algebraic systems hop topic. The braid groups, which are non-commutative, have attracted much attention as a new platform for constructing quantum attack-resistant cryptosystems. A ring signature scheme is proposed based on the difficulty of the root extraction problem over braid groups, which can resist existential forgery against the adaptively cho-sen-message attack under the random oracle model.
基金supported by the National Natural Science Foundation of China(No.11971112)。
文摘Motivated by the work of Birman about the relationship between mapping class groups and braid groups,the authors discuss the relationship between the orbit braid group and the equivariant mapping class group on the closed surface M with a free and proper group action in this paper.Their construction is based on the exact sequence given by the fibration F_(0)^(G) M→F(M/G,n).The conclusion is closely connected with the braid group of the quotient space.Comparing with the situation without the group action,there is a big difference when the quotient space is T^(2).
文摘We unify and generalize several approaches to constructing braid group representa-tions from finite groups,using iterated twisted tensor products.We provide some general characterizations and classification of these representations,focusing on the size of their images,which are typically finite groups.The well-studied Gaussian representations associated with metaplectic modular categories can be understood in this framework,and we give some new examples to illustrate their ubiquity.Our results suggest a relationship between the braiding on the G-gaugings of a pointed modular category C(A,Q)and that of C(A,Q)itself.
基金Project supported by the National Natural Science Foundation of China.
文摘A series of irreducible representations of braid group Bn are given.By means of a generalized Conway relation (gi-q)(gi+p) = 0,a complete set of operators H(i) are constructed.With the eigenvectors of H(i) as representation bases,the biparametric irreducible representations of Bn are obtained by the help of Yang diagrams.
文摘We survey various generalizations of braid groups for quivers with superpotential and focus on the cluster braid groups, which are introduced in a joint work with King (2018). Our motivations come from the study of cluster algebras, Calabi-Yau categories and Bridgeland stability conditions.
文摘A unit cell geometrical structure was found with the use of symmetry operations corresponding to the point group C3. Based on the symmetry of space group R3, a 3D braided geometrical structure was obtained by transforming the unit-cell. The features corresponding to this braided structure were studied. The fiber volume percentage and variational tendencies of the material were predicted by establishing a geometric model.
