For a given hereditary abelian category satisfying some finiteness conditions,in certain twisted cases it is shown that the modified Ringel-Hall algebra is isomorphic to the naive lattice algebra and there exists an e...For a given hereditary abelian category satisfying some finiteness conditions,in certain twisted cases it is shown that the modified Ringel-Hall algebra is isomorphic to the naive lattice algebra and there exists an epimorphism from the modified Ringel-Hall algebra to the lattice algebra.Furthermore,the kernel of this epimorphism is described explicitly.Finally,we show that the naive lattice algebra is invariant under the derived equivalences of hereditary abelian categories.展开更多
Let t be a positive integer and A be a hereditary abelian category satisfying some finiteness conditions.We define the semi-derived Ringel-Hall algebra of A from the category C_(Z/t)(A)of Z/t-graded complexes and obta...Let t be a positive integer and A be a hereditary abelian category satisfying some finiteness conditions.We define the semi-derived Ringel-Hall algebra of A from the category C_(Z/t)(A)of Z/t-graded complexes and obtain a natural basis of the semi-derived Ringel-Hall algebra.Moreover,we describe the semiderived Ringel-Hall algebra by the generators and defining relations.In particular,if t is an odd integer,we show an embedding of the derived Hall algebra of the odd-periodic relative derived category in the extended semi-derived Ringel-Hall algebra.展开更多
In this paper, we investigate some new traveling wave solutions to Vakhnenko-Parkes equation via three modified mathematical methods. The derived solutions have been obtained including periodic and solitons solutions ...In this paper, we investigate some new traveling wave solutions to Vakhnenko-Parkes equation via three modified mathematical methods. The derived solutions have been obtained including periodic and solitons solutions in the form of trigonometric, hyperbolic, and rational function solutions. The graphical representations of some solutions by assigning particular values to the parameters under prescribed conditions in each solutions and comparing of solutions with those gained by other authors indicate that these employed techniques are more effective, efficient and applicable mathematical tools for solving nonlinear problems in applied science.展开更多
In 2012, the author submitted an article to the Prespacetime Journal based upon the premise of inquiry as to the alleged vanishing of disjoint open sets contributing to quantum vector measures no longer working, i.e. ...In 2012, the author submitted an article to the Prespacetime Journal based upon the premise of inquiry as to the alleged vanishing of disjoint open sets contributing to quantum vector measures no longer working, i.e. the solution in 2012 was that the author stated that quantum measures in 4 dimensions would not work, mandating, if measure theory were used, imbedding in higher dimensions was necessary for a singularity. The idea was to use the methodology of String Theory as to come up with a way out of the impasse if higher dimensions do not exist. We revisit this question, taking into account a derived HUP, for metric tensors if we look at Pre-Planckian space-time introducing a pre-quantum mechanical HUP which may be a way to ascertain a solution not mandating higher dimensions, as well as introducing cautions as to what will disrupt the offered solution. Note that first, measurable spaces allow disjoint sets. Also, that smooth relations alone do not define separability or admit sets Planck’s length, if it exists, is a natural way to get about the “bad effects” of a cosmic singularity at the beginning of space-time evolution, but if a development is to be believed, namely by Stoica in the article, about removing the cosmic singularity as a breakdown point in relativity, there is nothing which forbids space-time from collapsing to a point. Without the use of a Pre Planckian HUP, for metric tensors, the quantum measures in four dimensions break down. We try to ascertain if a Pre Planckian HUP is sufficient to avoid this pathology and also look at if division algebras which can link Octonionic geometry and E8, to Quark spinors, in the standard model and add sufficient definition to the standard model are necessary and sufficient conditions for a metric tensor HUP which may remove this breakdown of the sum rule in the onset of the “Big Bang”.展开更多
In the present paper we describe a specialization of prinjective Ringel-Hall algebra to 1, for prinjective modules over incidence algebras of posets of finite prinjective type, by generators and relations. This gives ...In the present paper we describe a specialization of prinjective Ringel-Hall algebra to 1, for prinjective modules over incidence algebras of posets of finite prinjective type, by generators and relations. This gives us a generalisation of Serre relations for semisimple Lie algebras. Connections of prinjective Ringel-Hall algebras with classical Lie algebras are also discussed.展开更多
This paper is devoted to the study of the structure of the double Ringel-Hall algebra D（A） for an infinite dimensional hereditary algebra A, which is given by a valued quiver F over a finite field, and also to the ...This paper is devoted to the study of the structure of the double Ringel-Hall algebra D（A） for an infinite dimensional hereditary algebra A, which is given by a valued quiver F over a finite field, and also to the study of the relations of D（A）-modules with representations of valued quiver Г.展开更多
In this paper,we consider a possible modification of the de Sitter and anti-de Sitter space for the extended uncertainty principle.For the modified anti-de Sitter model we discuss the representation and wave functions...In this paper,we consider a possible modification of the de Sitter and anti-de Sitter space for the extended uncertainty principle.For the modified anti-de Sitter model we discuss the representation and wave functions of the momentum operator for a one-dimensional box problem.Also,we consider modified Snyder and anti-Snyder models for the generalized uncertainty principle.Then,we assume the Hamiltonian with different potential and solve the Heisenberg algebra for the modified(anti)-de Sitter and(anti)-Snyder models in both position and in the momentum space.展开更多
In the present paper we investigate prinjective Ringel-Hall algebras, for prinjective modules over incidence algebras of posers of finite prinjective type. Results we obtain are analogous to these, given by C. M. Ring...In the present paper we investigate prinjective Ringel-Hall algebras, for prinjective modules over incidence algebras of posers of finite prinjective type. Results we obtain are analogous to these, given by C. M. Ringel, for representations of Dynkin quivers. In particular we give a description of prinjective Ringel-Hall algebras by generators and relations.展开更多
For a symmetrizable Kac-Moody Lie algebra g, Lusztig introduced the corresponding modified quantized enveloping algebra˙U and its canonical basis˙B given by Lusztig in 1992. In this paper, in the case that g is a sy...For a symmetrizable Kac-Moody Lie algebra g, Lusztig introduced the corresponding modified quantized enveloping algebra˙U and its canonical basis˙B given by Lusztig in 1992. In this paper, in the case that g is a symmetric Kac-Moody Lie algebra of finite or affine type, the authors define a set M which depends only on the root category R and prove that there is a bijection between M and ˙B, where R is the T^2-orbit category of the bounded derived category of the corresponding Dynkin or tame quiver. The method in this paper is based on a result of Lin, Xiao and Zhang in 2011, which gives a PBW-type basis of U^+.展开更多
Let U be a quantized enveloping algebra and U its modified form. Lusztig gives some symmetries on U and U. In view of the realization of U by the reduced Drinfeld double of the Ringel- Hall algebra, one can apply the ...Let U be a quantized enveloping algebra and U its modified form. Lusztig gives some symmetries on U and U. In view of the realization of U by the reduced Drinfeld double of the Ringel- Hall algebra, one can apply the BGP-refiection functors to the double Ringel-HM1 algebra to obtain Lusztig＇s symmetries on U and their important properties, for instance, the braid relations. In this paper, we define a modified form Hof the Ringel-Hall algebra and realize the Lusztig＇s symmetries on U by applying the BGP-reflection functors to H展开更多
In this paper, by using the Frobenius morphism and the multiplication formulas of the generic extension monoid algebra, the authors first give a presentation of the degenerate Ringel-Hall algebra, and then construct t...In this paper, by using the Frobenius morphism and the multiplication formulas of the generic extension monoid algebra, the authors first give a presentation of the degenerate Ringel-Hall algebra, and then construct the Gr¨obner-Shirshov basis for degenerate Ringel-Hall algebras of type F_4.展开更多
基金supported by National Natural Science Foundation of China(Grant No.11701473)Youth Talent Foundation of Fuyang Normal University(Grant No.rcxm201803)。
文摘For a given hereditary abelian category satisfying some finiteness conditions,in certain twisted cases it is shown that the modified Ringel-Hall algebra is isomorphic to the naive lattice algebra and there exists an epimorphism from the modified Ringel-Hall algebra to the lattice algebra.Furthermore,the kernel of this epimorphism is described explicitly.Finally,we show that the naive lattice algebra is invariant under the derived equivalences of hereditary abelian categories.
基金supported by National Natural Science Foundation of China(Grant Nos.12001107 and 11821001)University Natural Science Project of Anhui Province(Grant No.KJ2021A0661)+1 种基金University Outstanding Youth Research Project in Anhui Province(Grant No.2022AH020082)Scientific Research and Innovation Team Project of Fuyang Normal University(Grant No.TDJC2021009)。
文摘Let t be a positive integer and A be a hereditary abelian category satisfying some finiteness conditions.We define the semi-derived Ringel-Hall algebra of A from the category C_(Z/t)(A)of Z/t-graded complexes and obtain a natural basis of the semi-derived Ringel-Hall algebra.Moreover,we describe the semiderived Ringel-Hall algebra by the generators and defining relations.In particular,if t is an odd integer,we show an embedding of the derived Hall algebra of the odd-periodic relative derived category in the extended semi-derived Ringel-Hall algebra.
文摘In this paper, we investigate some new traveling wave solutions to Vakhnenko-Parkes equation via three modified mathematical methods. The derived solutions have been obtained including periodic and solitons solutions in the form of trigonometric, hyperbolic, and rational function solutions. The graphical representations of some solutions by assigning particular values to the parameters under prescribed conditions in each solutions and comparing of solutions with those gained by other authors indicate that these employed techniques are more effective, efficient and applicable mathematical tools for solving nonlinear problems in applied science.
文摘In 2012, the author submitted an article to the Prespacetime Journal based upon the premise of inquiry as to the alleged vanishing of disjoint open sets contributing to quantum vector measures no longer working, i.e. the solution in 2012 was that the author stated that quantum measures in 4 dimensions would not work, mandating, if measure theory were used, imbedding in higher dimensions was necessary for a singularity. The idea was to use the methodology of String Theory as to come up with a way out of the impasse if higher dimensions do not exist. We revisit this question, taking into account a derived HUP, for metric tensors if we look at Pre-Planckian space-time introducing a pre-quantum mechanical HUP which may be a way to ascertain a solution not mandating higher dimensions, as well as introducing cautions as to what will disrupt the offered solution. Note that first, measurable spaces allow disjoint sets. Also, that smooth relations alone do not define separability or admit sets Planck’s length, if it exists, is a natural way to get about the “bad effects” of a cosmic singularity at the beginning of space-time evolution, but if a development is to be believed, namely by Stoica in the article, about removing the cosmic singularity as a breakdown point in relativity, there is nothing which forbids space-time from collapsing to a point. Without the use of a Pre Planckian HUP, for metric tensors, the quantum measures in four dimensions break down. We try to ascertain if a Pre Planckian HUP is sufficient to avoid this pathology and also look at if division algebras which can link Octonionic geometry and E8, to Quark spinors, in the standard model and add sufficient definition to the standard model are necessary and sufficient conditions for a metric tensor HUP which may remove this breakdown of the sum rule in the onset of the “Big Bang”.
文摘In the present paper we describe a specialization of prinjective Ringel-Hall algebra to 1, for prinjective modules over incidence algebras of posets of finite prinjective type, by generators and relations. This gives us a generalisation of Serre relations for semisimple Lie algebras. Connections of prinjective Ringel-Hall algebras with classical Lie algebras are also discussed.
基金Project supported by the National Natural Science Foundation of China (No.10471071) the 973 Project of the Ministry of Science and Technology of China.
文摘This paper is devoted to the study of the structure of the double Ringel-Hall algebra D（A） for an infinite dimensional hereditary algebra A, which is given by a valued quiver F over a finite field, and also to the study of the relations of D（A）-modules with representations of valued quiver Г.
文摘In this paper,we consider a possible modification of the de Sitter and anti-de Sitter space for the extended uncertainty principle.For the modified anti-de Sitter model we discuss the representation and wave functions of the momentum operator for a one-dimensional box problem.Also,we consider modified Snyder and anti-Snyder models for the generalized uncertainty principle.Then,we assume the Hamiltonian with different potential and solve the Heisenberg algebra for the modified(anti)-de Sitter and(anti)-Snyder models in both position and in the momentum space.
文摘In the present paper we investigate prinjective Ringel-Hall algebras, for prinjective modules over incidence algebras of posers of finite prinjective type. Results we obtain are analogous to these, given by C. M. Ringel, for representations of Dynkin quivers. In particular we give a description of prinjective Ringel-Hall algebras by generators and relations.
基金supported by the Fundamental Research Funds for the Central Universities(No.BLX2013014)the National Natural Science Foundation of China(No.11131001)
文摘For a symmetrizable Kac-Moody Lie algebra g, Lusztig introduced the corresponding modified quantized enveloping algebra˙U and its canonical basis˙B given by Lusztig in 1992. In this paper, in the case that g is a symmetric Kac-Moody Lie algebra of finite or affine type, the authors define a set M which depends only on the root category R and prove that there is a bijection between M and ˙B, where R is the T^2-orbit category of the bounded derived category of the corresponding Dynkin or tame quiver. The method in this paper is based on a result of Lin, Xiao and Zhang in 2011, which gives a PBW-type basis of U^+.
基金Supported by National Natural Science Foundation of China(Grant No.11131001)the Fundamental Research Funds for the Central Universities(Grant No.BLX2013014)
文摘Let U be a quantized enveloping algebra and U its modified form. Lusztig gives some symmetries on U and U. In view of the realization of U by the reduced Drinfeld double of the Ringel- Hall algebra, one can apply the BGP-refiection functors to the double Ringel-HM1 algebra to obtain Lusztig＇s symmetries on U and their important properties, for instance, the braid relations. In this paper, we define a modified form Hof the Ringel-Hall algebra and realize the Lusztig＇s symmetries on U by applying the BGP-reflection functors to H
基金supported by the National Natural Science Foundation of China(Nos.11361056,11271043,11471186)
文摘In this paper, by using the Frobenius morphism and the multiplication formulas of the generic extension monoid algebra, the authors first give a presentation of the degenerate Ringel-Hall algebra, and then construct the Gr¨obner-Shirshov basis for degenerate Ringel-Hall algebras of type F_4.
