Let N be a nest of projections on a Hilbert space H and T(N) be the corresponding nest algebra. Let A be a large subalgebra of T(N). It is proved that any maximal n-nilpotent ideal of A is in the form of A∩R F,where...Let N be a nest of projections on a Hilbert space H and T(N) be the corresponding nest algebra. Let A be a large subalgebra of T(N). It is proved that any maximal n-nilpotent ideal of A is in the form of A∩R F,where F is a finite subnest of N and R F is the Jacobson radical of T(F).Using this result can prove that two large subalgebras are isomorphic if and only if the corresponding nests are similar.展开更多
Let P be a parabolic subalgebra of a general linear Lie algebra gl（n,F） over a field F, where n ≥ 3, F contains at least n different elements, and char（F） ≠ 2. In this article, we prove that generalized derivati...Let P be a parabolic subalgebra of a general linear Lie algebra gl（n,F） over a field F, where n ≥ 3, F contains at least n different elements, and char（F） ≠ 2. In this article, we prove that generalized derivations, quasiderivations, and product zero derivations of P coincide, and any generalized derivation of P is a sum of an inner derivation, a central quasiderivation, and a scalar multiplication map of P. We also show that any commuting automorphism of P is a central automorphism, and any commuting derivation of P is a central derivation.展开更多
In this paper, we determine all maximal graded subalgebras of the general linear Lie superalgebras containing the standard Cartan subalgebras over a unital supercommutative superring with 2 invertible.
In this paper, we prove the nonimbedding theorem in nilpotent n-Lie algebras which is an analogue to the nonimbedding theorem of Burnsids in groups of prime power order. We also study the properties of Frattini subalg...In this paper, we prove the nonimbedding theorem in nilpotent n-Lie algebras which is an analogue to the nonimbedding theorem of Burnsids in groups of prime power order. We also study the properties of Frattini subalgebras of n-Lie algebras over the field with characteristic zero, and prove that the Frattini subalgebra of any k-solvable （k ≥2） n-Lie algebra is zero.展开更多
In this note by two relations belonging to (∈) and quasi-coincidence (q) between fuzzy points and fuzzy sets, the notion of (α,β)-fuzzy Q-algebras, the level Q-subalgebra is introduced where α,β are any two of {...In this note by two relations belonging to (∈) and quasi-coincidence (q) between fuzzy points and fuzzy sets, the notion of (α,β)-fuzzy Q-algebras, the level Q-subalgebra is introduced where α,β are any two of {∈,q,∈∨q,∈∧q} with α≠∈∧q. Then we state and prove some theorems which determine the relationship between these notions and Q-subalgebras. The images and inverse images of (α,β)-fuzzy Q-subalgebras are defined, and how the homomorphic images and inverse images of (α,β)-fuzzy Q-subalgebra becomes (α,β)-fuzzy Q-algebras are studied.展开更多
Using the defining matrices of A1 in classical algebras An, Bn, Cn and Dn, deduce the embedding indices of the physical A1 algebra in classical algebras, The Ginocchio so(8) model is as an example.
Let G be a finite group, H ≤ G and R be a commutative ring with an identity 1R. Let CRG（H）={α ∈ RG｜αh = hα for all h ∈ H）, which is called the centralizer subalgebra of H in RG. Obviously, if H=G then CRG（H...Let G be a finite group, H ≤ G and R be a commutative ring with an identity 1R. Let CRG（H）={α ∈ RG｜αh = hα for all h ∈ H）, which is called the centralizer subalgebra of H in RG. Obviously, if H=G then CRG（H） is just the central subalgebra Z（RG） of RG. In this note, we show that the set of all H- conjugacy class sums of G forms an R-basis of CRG（H）. Furthermore, let N be a normal subgroup of G and γthe natural epimorphism from G to G to G/N. Then γ induces an epimorphism from RG to RG, also denoted by % We also show that if R is a field of characteristic zero, then γ induces an epimorphism from CRG（H） to CRG（H）, that is, 7（CRG（H）） = CRG（H）.展开更多
Let g be the general linear Lie algebra consisting of all n x n matrices over a field F and with the usual bracket operation {x, y} =xy - yx. An invertible map φ ： g →g is said to preserve staircase subalgebras if ...Let g be the general linear Lie algebra consisting of all n x n matrices over a field F and with the usual bracket operation {x, y} =xy - yx. An invertible map φ ： g →g is said to preserve staircase subalgebras if it maps every staircase subalgebra to some staircase subalgebra of the same dimension. In this paper, we devote to giving an explicit description on the invertible maps on g that preserve staircase subalgebras.展开更多
There are three subalgebra chains in Ginocchlo's so(8)model.The subalgebra so(5)+su(2)and so(7)are maximum subalgebras in so(8).The subalgebra so(6)is not this case.We can find a new subalgebra so(7)between the so...There are three subalgebra chains in Ginocchlo's so(8)model.The subalgebra so(5)+su(2)and so(7)are maximum subalgebras in so(8).The subalgebra so(6)is not this case.We can find a new subalgebra so(7)between the so(8)and so(6).It is useful in the calculation at least.展开更多
Let A be an infinite dimensional stably finite unital simple separable C^(*)-algebra.Let B■A be a stably(centrally)large subalgebra in A such that B is m-almost divisible(m-almost divisible,weakly(m,n)-divisible).The...Let A be an infinite dimensional stably finite unital simple separable C^(*)-algebra.Let B■A be a stably(centrally)large subalgebra in A such that B is m-almost divisible(m-almost divisible,weakly(m,n)-divisible).Then A is 2(m+1)-almost divisible(weakly m-almost divisible,secondly weakly(m,n)-divisible).展开更多
A map φ on a Lie algebra g is called to be commuting if [φ(x), x] = 0 for all x ∈ g. Let L be a finite-dimensional simple Lie algebra over an algebraically closed field F of characteristic 0, P a parabolic subalgeb...A map φ on a Lie algebra g is called to be commuting if [φ(x), x] = 0 for all x ∈ g. Let L be a finite-dimensional simple Lie algebra over an algebraically closed field F of characteristic 0, P a parabolic subalgebra of L. In this paper, we prove that a linear mapφon P is commuting if and only if φ is a scalar multiplication map on P.展开更多
First, we reviewed the definitions of lattice implication algebras, lattice implication subalgebras, and LI-ideals, and provided an equivalent definition of LI-ideal. Then we investigated some properties of lattice im...First, we reviewed the definitions of lattice implication algebras, lattice implication subalgebras, and LI-ideals, and provided an equivalent definition of LI-ideal. Then we investigated some properties of lattice implication subalgebra and U-ideal, and found the least lattice implication subalgebra. Finally, the relation between lattice implication subalgebra and LI-ideal is presented. It is proved that no LI-ideals are non-trivial lattice implication subalgebras.展开更多
Having realized various significant roles that higher-dimensional nonlinear partial differ-ential equations(NLPDEs)play in engineering,we analytically investigate in this paper,a higher-dimensional soliton equation,wi...Having realized various significant roles that higher-dimensional nonlinear partial differ-ential equations(NLPDEs)play in engineering,we analytically investigate in this paper,a higher-dimensional soliton equation,with applications particularly in ocean physics and mechatronics(electrical electronics and mechanical)engineering.Infinitesimal generators of Lie point symmetries of the equation are computed using Lie group analysis of differen-tial equations.In addition,we construct commutation as well as Lie adjoint representation tables for the nine-dimensional Lie algebra achieved.Further,a one-dimensional optimal system of Lie subalgebras is also presented for the soliton equation.This consequently enables us to generate abundant group-invariant solutions through the reduction of the understudy equation into various ordinary differential equations(ODEs).On solving the achieved nonlinear differential equations,we secure various solitonic solutions.In conse-quence,these solutions containing diverse mathematical functions furnish copious shapes of dynamical wave structures,ranging from periodic,kink and kink-shaped nanopteron,soliton(bright and dark)to breather waves with extensive wave collisions depicted.We physically interpreted the resulting soliton solutions by imploring graphical depictions in three dimensions,two dimensions and density plots.Moreover,the gained group-invariant solutions involved several arbitrary functions,thus exhibiting rich physical structures.We also implore the power series technique to solve part of the complicated differential equa-tions and give valid comments on their results.Later,we outline some applications of our results in ocean physics and mechatronics engineering.展开更多
In this paper, we first prove that the dual module of a rational module is still a rational module, and maximum rational modules keep their exac t properties. Then, we give the Maschke theorem of the coideal subalge...In this paper, we first prove that the dual module of a rational module is still a rational module, and maximum rational modules keep their exac t properties. Then, we give the Maschke theorem of the coideal subalgebra of qua si-Frobenius algebra, and give some equivalent conditions for the ideal subcoal gebra.展开更多
文摘Let N be a nest of projections on a Hilbert space H and T(N) be the corresponding nest algebra. Let A be a large subalgebra of T(N). It is proved that any maximal n-nilpotent ideal of A is in the form of A∩R F,where F is a finite subnest of N and R F is the Jacobson radical of T(F).Using this result can prove that two large subalgebras are isomorphic if and only if the corresponding nests are similar.
基金supported by the National Natural Science Foundation of China(11101084,11071040)the Fujian Province Nature Science Foundation of China(2013J01005)
文摘Let P be a parabolic subalgebra of a general linear Lie algebra gl（n,F） over a field F, where n ≥ 3, F contains at least n different elements, and char（F） ≠ 2. In this article, we prove that generalized derivations, quasiderivations, and product zero derivations of P coincide, and any generalized derivation of P is a sum of an inner derivation, a central quasiderivation, and a scalar multiplication map of P. We also show that any commuting automorphism of P is a central automorphism, and any commuting derivation of P is a central derivation.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1117105511471090)the Natural Science Foundation of the Education Department of Heilongjiang Province(Grant No.12521158)
文摘In this paper, we determine all maximal graded subalgebras of the general linear Lie superalgebras containing the standard Cartan subalgebras over a unital supercommutative superring with 2 invertible.
基金The NSF(2005000088)of Hebei Province the NSF(y2004034)of Hebei University.
文摘In this paper, we prove the nonimbedding theorem in nilpotent n-Lie algebras which is an analogue to the nonimbedding theorem of Burnsids in groups of prime power order. We also study the properties of Frattini subalgebras of n-Lie algebras over the field with characteristic zero, and prove that the Frattini subalgebra of any k-solvable （k ≥2） n-Lie algebra is zero.
文摘In this note by two relations belonging to (∈) and quasi-coincidence (q) between fuzzy points and fuzzy sets, the notion of (α,β)-fuzzy Q-algebras, the level Q-subalgebra is introduced where α,β are any two of {∈,q,∈∨q,∈∧q} with α≠∈∧q. Then we state and prove some theorems which determine the relationship between these notions and Q-subalgebras. The images and inverse images of (α,β)-fuzzy Q-subalgebras are defined, and how the homomorphic images and inverse images of (α,β)-fuzzy Q-subalgebra becomes (α,β)-fuzzy Q-algebras are studied.
文摘Using the defining matrices of A1 in classical algebras An, Bn, Cn and Dn, deduce the embedding indices of the physical A1 algebra in classical algebras, The Ginocchio so(8) model is as an example.
基金The NSF(11071155) of Chinathe NSF(2008A03) of Shandong Province
文摘Let G be a finite group, H ≤ G and R be a commutative ring with an identity 1R. Let CRG（H）={α ∈ RG｜αh = hα for all h ∈ H）, which is called the centralizer subalgebra of H in RG. Obviously, if H=G then CRG（H） is just the central subalgebra Z（RG） of RG. In this note, we show that the set of all H- conjugacy class sums of G forms an R-basis of CRG（H）. Furthermore, let N be a normal subgroup of G and γthe natural epimorphism from G to G to G/N. Then γ induces an epimorphism from RG to RG, also denoted by % We also show that if R is a field of characteristic zero, then γ induces an epimorphism from CRG（H） to CRG（H）, that is, 7（CRG（H）） = CRG（H）.
基金The NSF (11126121) of ChinaPh.D.Fund (B2010-93) of Henan Polytechnic University+1 种基金Natural Science Research Program (112300410120) of Science and Technology Department of Henan ProvinceNatural Science Research Program (2011B110016) of Education Department of Henan Province
文摘Let g be the general linear Lie algebra consisting of all n x n matrices over a field F and with the usual bracket operation {x, y} =xy - yx. An invertible map φ ： g →g is said to preserve staircase subalgebras if it maps every staircase subalgebra to some staircase subalgebra of the same dimension. In this paper, we devote to giving an explicit description on the invertible maps on g that preserve staircase subalgebras.
基金Supported by the Science Fund of the Chinese Acadamy of Sciences。
文摘There are three subalgebra chains in Ginocchlo's so(8)model.The subalgebra so(5)+su(2)and so(7)are maximum subalgebras in so(8).The subalgebra so(6)is not this case.We can find a new subalgebra so(7)between the so(8)and so(6).It is useful in the calculation at least.
基金supported by National Natural Sciences Foundation of China(11501357,11571008)supported by National Natural Sciences Foundation of China(11871375)。
文摘Let A be an infinite dimensional stably finite unital simple separable C^(*)-algebra.Let B■A be a stably(centrally)large subalgebra in A such that B is m-almost divisible(m-almost divisible,weakly(m,n)-divisible).Then A is 2(m+1)-almost divisible(weakly m-almost divisible,secondly weakly(m,n)-divisible).
基金Supported by the National Natural Science Foundation of China（Ill01084） Supported by the Fujian Province Natural Science Foundation of China
文摘A map φ on a Lie algebra g is called to be commuting if [φ(x), x] = 0 for all x ∈ g. Let L be a finite-dimensional simple Lie algebra over an algebraically closed field F of characteristic 0, P a parabolic subalgebra of L. In this paper, we prove that a linear mapφon P is commuting if and only if φ is a scalar multiplication map on P.
基金The National Natural Science Foundationof China (No.60875034)the Specialized Research Fundfor the Doctoral Program of Higher Education of China (No.20060613007)
文摘First, we reviewed the definitions of lattice implication algebras, lattice implication subalgebras, and LI-ideals, and provided an equivalent definition of LI-ideal. Then we investigated some properties of lattice implication subalgebra and U-ideal, and found the least lattice implication subalgebra. Finally, the relation between lattice implication subalgebra and LI-ideal is presented. It is proved that no LI-ideals are non-trivial lattice implication subalgebras.
基金the North-West University,Mafikeng campus for its continued support.
文摘Having realized various significant roles that higher-dimensional nonlinear partial differ-ential equations(NLPDEs)play in engineering,we analytically investigate in this paper,a higher-dimensional soliton equation,with applications particularly in ocean physics and mechatronics(electrical electronics and mechanical)engineering.Infinitesimal generators of Lie point symmetries of the equation are computed using Lie group analysis of differen-tial equations.In addition,we construct commutation as well as Lie adjoint representation tables for the nine-dimensional Lie algebra achieved.Further,a one-dimensional optimal system of Lie subalgebras is also presented for the soliton equation.This consequently enables us to generate abundant group-invariant solutions through the reduction of the understudy equation into various ordinary differential equations(ODEs).On solving the achieved nonlinear differential equations,we secure various solitonic solutions.In conse-quence,these solutions containing diverse mathematical functions furnish copious shapes of dynamical wave structures,ranging from periodic,kink and kink-shaped nanopteron,soliton(bright and dark)to breather waves with extensive wave collisions depicted.We physically interpreted the resulting soliton solutions by imploring graphical depictions in three dimensions,two dimensions and density plots.Moreover,the gained group-invariant solutions involved several arbitrary functions,thus exhibiting rich physical structures.We also implore the power series technique to solve part of the complicated differential equa-tions and give valid comments on their results.Later,we outline some applications of our results in ocean physics and mechatronics engineering.
文摘In this paper, we first prove that the dual module of a rational module is still a rational module, and maximum rational modules keep their exac t properties. Then, we give the Maschke theorem of the coideal subalgebra of qua si-Frobenius algebra, and give some equivalent conditions for the ideal subcoal gebra.
