报道了发现于浙江省宁波市象山的1种浙江新记录植物——田葱Philydrum lanuginosum Banks et Sol.ex Gaertn.,田葱属Philydrum Banks et Sol.ex Gaertn.及田葱科Philydraceae均为浙江省分布新记录;并对该种的来源进行了考证,描述了形态...报道了发现于浙江省宁波市象山的1种浙江新记录植物——田葱Philydrum lanuginosum Banks et Sol.ex Gaertn.,田葱属Philydrum Banks et Sol.ex Gaertn.及田葱科Philydraceae均为浙江省分布新记录;并对该种的来源进行了考证,描述了形态特征、生境、伴生植物及用途。凭证标本藏于浙江农林大学植物标本馆(ZJFC)。展开更多
We categorify the notion of coalgebras by imposing a co-associative law up to some isomorphisms on theco-multiplication map and requiring that these isomorphisms satisfy certain law of their own,which is called the co...We categorify the notion of coalgebras by imposing a co-associative law up to some isomorphisms on theco-multiplication map and requiring that these isomorphisms satisfy certain law of their own,which is called the copentagonidentity.We also set up a 2-category of 2-coalgebras.The purpose of this study is from the idea of reconsideringthe quasi-Hopf algebras by the categoriScation process,so that we can study the theory of quasi-Hopf algebras and theirrepresentations in some new framework of higher category theory in naturai ways.展开更多
In this paper,we study the diagrammatic categorification of the fermion algebra.We construct a graphical category corresponding to the one-dimensional(1D) fermion algebra,and we investigate the properties of this cate...In this paper,we study the diagrammatic categorification of the fermion algebra.We construct a graphical category corresponding to the one-dimensional(1D) fermion algebra,and we investigate the properties of this category.The categorical analogues of the Fock states are some kind of 1-morphisms in our category,and the dimension of the vector space of 2-morphisms is exactly the inner product of the corresponding Fock states.All the results in our categorical framework coincide exactly with those in normal quantum mechanics.展开更多
In this paper, we categorify the algebra U_q(sl_2) with the same approach as in [A. Lauda, Adv. Math. (2010), arXiv:math.QA/0803.3652; M. Khovanov, Comm. Algebra 11 (2001) 5033]. The algebra =_q(sl_2) is obtained ...In this paper, we categorify the algebra U_q(sl_2) with the same approach as in [A. Lauda, Adv. Math. (2010), arXiv:math.QA/0803.3652; M. Khovanov, Comm. Algebra 11 (2001) 5033]. The algebra =_q(sl_2) is obtained from U_q(sl_2) by adjoining a collection of orthogonal idempotents 1_λ, λ∈P, in which P is the weight lattice of U_q(sl_2). Under such construction the algebra U is decomposed into a direct sum _(λ∈P) 1_λ,U1_λ. We set the collection of λ∈ P as the objects of the category u, 1-morphisms from λ to λ' are given by 1_λ,U1_λ, and 2-morphisms are constructed by some semilinear form defined on U. Hence we get a 2-category u from the algebra U_q(sl_2).展开更多
In this paper, we lift Fermions to functors acting on some homotopy category by the Boson–Fermion correspondence and get the categorified relations of Fermions. In this way, both the categorified Bosons and the categ...In this paper, we lift Fermions to functors acting on some homotopy category by the Boson–Fermion correspondence and get the categorified relations of Fermions. In this way, both the categorified Bosons and the categorified Fermions can be viewed as functors on the same category. We also give actions of these functors on the charged Young diagrams(or equivalently, Maya diagrams), so that the classical theory of Boson–Fermion correspondence is very well recovered as a result of such a categorification.展开更多
In this paper a set of generalized descent equations are proposed. The solutions to those descent equations labeled by r for any r(r ≥ 2, r ∈ N) are forms of degrees varying from 0 to(2r-1). And the case of r = 2 is...In this paper a set of generalized descent equations are proposed. The solutions to those descent equations labeled by r for any r(r ≥ 2, r ∈ N) are forms of degrees varying from 0 to(2r-1). And the case of r = 2 is mainly discussed.展开更多
文摘报道了发现于浙江省宁波市象山的1种浙江新记录植物——田葱Philydrum lanuginosum Banks et Sol.ex Gaertn.,田葱属Philydrum Banks et Sol.ex Gaertn.及田葱科Philydraceae均为浙江省分布新记录;并对该种的来源进行了考证,描述了形态特征、生境、伴生植物及用途。凭证标本藏于浙江农林大学植物标本馆(ZJFC)。
基金Supported by National Natural Science Foundation of China under Grant Nos. 10975102, 11031005 10871135, 10871227, and PHR201007107
文摘We categorify the notion of coalgebras by imposing a co-associative law up to some isomorphisms on theco-multiplication map and requiring that these isomorphisms satisfy certain law of their own,which is called the copentagonidentity.We also set up a 2-category of 2-coalgebras.The purpose of this study is from the idea of reconsideringthe quasi-Hopf algebras by the categoriScation process,so that we can study the theory of quasi-Hopf algebras and theirrepresentations in some new framework of higher category theory in naturai ways.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10975102,10871135,11031005,and 11075014)
文摘In this paper,we study the diagrammatic categorification of the fermion algebra.We construct a graphical category corresponding to the one-dimensional(1D) fermion algebra,and we investigate the properties of this category.The categorical analogues of the Fock states are some kind of 1-morphisms in our category,and the dimension of the vector space of 2-morphisms is exactly the inner product of the corresponding Fock states.All the results in our categorical framework coincide exactly with those in normal quantum mechanics.
基金Supported by National Natural Science Foundation of China under Grant Nos. 10975102, 10871135, 11031005, and 10871227
文摘In this paper, we categorify the algebra U_q(sl_2) with the same approach as in [A. Lauda, Adv. Math. (2010), arXiv:math.QA/0803.3652; M. Khovanov, Comm. Algebra 11 (2001) 5033]. The algebra =_q(sl_2) is obtained from U_q(sl_2) by adjoining a collection of orthogonal idempotents 1_λ, λ∈P, in which P is the weight lattice of U_q(sl_2). Under such construction the algebra U is decomposed into a direct sum _(λ∈P) 1_λ,U1_λ. We set the collection of λ∈ P as the objects of the category u, 1-morphisms from λ to λ' are given by 1_λ,U1_λ, and 2-morphisms are constructed by some semilinear form defined on U. Hence we get a 2-category u from the algebra U_q(sl_2).
基金Supported by National Nature Science Foundation of China under Grant Nos.11031005 and 11475116Beijing Municipal Commission of Education under Grant Nos.KZ201210028032 and KZ201410028033
文摘In this paper, we lift Fermions to functors acting on some homotopy category by the Boson–Fermion correspondence and get the categorified relations of Fermions. In this way, both the categorified Bosons and the categorified Fermions can be viewed as functors on the same category. We also give actions of these functors on the charged Young diagrams(or equivalently, Maya diagrams), so that the classical theory of Boson–Fermion correspondence is very well recovered as a result of such a categorification.
基金Supported by National Natural Science Foundation of China under Grant Nos.11475116,11401400
文摘In this paper a set of generalized descent equations are proposed. The solutions to those descent equations labeled by r for any r(r ≥ 2, r ∈ N) are forms of degrees varying from 0 to(2r-1). And the case of r = 2 is mainly discussed.
