The polynomial algebra is a deformed su（2） algebra. Here, we use polynomial algebra az a method to solve a series of deformed oscillators. Thus, we find a series of physics systems corresponding with polynomial alge...The polynomial algebra is a deformed su（2） algebra. Here, we use polynomial algebra az a method to solve a series of deformed oscillators. Thus, we find a series of physics systems corresponding with polynomial algebra with different highest orders.展开更多
The filtered-graded transfer of SAGBI bases computation in solvable polynomial algebras was considered. The relations among the SAGBI bases of a subalgebra B, its associated graded algebra G(B) and Rees algebra B were...The filtered-graded transfer of SAGBI bases computation in solvable polynomial algebras was considered. The relations among the SAGBI bases of a subalgebra B, its associated graded algebra G(B) and Rees algebra B were got. These relations solve a natural question: how to determine the generating set of G(B) and B from any given generating set of B. Based on these some equivalent conditions for the existence of finite SAGBI bases can be got.展开更多
In this study, particular matrices which is called P-matrices were defined for the action of the Steenrod powers on the polynomial algebra and it was shown that they can be used to calculate the action of Steenrod pow...In this study, particular matrices which is called P-matrices were defined for the action of the Steenrod powers on the polynomial algebra and it was shown that they can be used to calculate the action of Steenrod powers on product of two generators. Finally an algorithm was given to obtain these matrices.展开更多
Let P-n be an algebraic polynomial of degree n with real coefficients. We study the extremal properties of the integral integral(-1)(1)(P ''(n) (x))(2)dx and integral(-1)(1) (1-x(2))1/2(P ''(n)(x))(2)d...Let P-n be an algebraic polynomial of degree n with real coefficients. We study the extremal properties of the integral integral(-1)(1)(P ''(n) (x))(2)dx and integral(-1)(1) (1-x(2))1/2(P ''(n)(x))(2)dx subject to the constraint max \P-n(x)\less than or equal to 1.展开更多
Framed links in thickened torus is studied. We give an expression of torus knot in the Kauffman bracket skein algebra. From this expression and using the theory of Gr？bner bases, we drive the reduced polynomial of a ...Framed links in thickened torus is studied. We give an expression of torus knot in the Kauffman bracket skein algebra. From this expression and using the theory of Gr？bner bases, we drive the reduced polynomial of a framed link, which is an ambient isotopic invariant and can be computed feasibly.展开更多
An enhaned NTRU cryptosystem eliminating decryption failures is proposed without using padding schemes and can resist the oracle model andchosen-ciphertext attacks. Because lattice reduction is the main threat to latt...An enhaned NTRU cryptosystem eliminating decryption failures is proposed without using padding schemes and can resist the oracle model andchosen-ciphertext attacks. Because lattice reduction is the main threat to lattice-based cryptosystems, lattice reductionalgorithms are analyzed to evaluate the security of this scheme. Furthermore, the new scheme remains the advantage of high efficiency of original NTRU.展开更多
In our earlier paper,we generalize the one-parameter(c)family of inhomogeneous firstorder differential operator representations of the orthogonal Lie algebras arising from conformal transformations to those of orthosy...In our earlier paper,we generalize the one-parameter(c)family of inhomogeneous firstorder differential operator representations of the orthogonal Lie algebras arising from conformal transformations to those of orthosymplectic Lie super algebras,and determine the irreducible condition.This paper deals with the cases when the irreducible condition fails.We prove that if n-m-1>0 and c is an integer satisfying 1≤c≤n-m-1,the representation of osp(2n+2|2m)has a composition series of length 2,and when n-m-1≥0 and c∈-N,the representation of osp(2n+2|2m)has a composition series of length 3,where N is the set of nonnegative integers.Moreover,we show that if c∈(max{n-m,0}-1/2-N)∪(-N),the representation of osp(2n+3|2m)has a composition series of length 2.In particular,we obtain an explicit presentation of the irreducible module with highest weight lλ2-λ1,where l is any positive integer and it is not a generalized Verma module.展开更多
Let A = F [x, y] be the polynomial algebra on two variables x, y over an algebraically closed field F of characteristic zero. Under the Poisson bracket, A is equipped with a natural Lie algebra structure. It is proven...Let A = F [x, y] be the polynomial algebra on two variables x, y over an algebraically closed field F of characteristic zero. Under the Poisson bracket, A is equipped with a natural Lie algebra structure. It is proven that the maximal good subspace of A* induced from the multiplication of the associative commutative algebra A coincides with the maximal good subspace of A* induced from the Poisson bracket of the Poisson Lie algebra A. Based on this, structures of dual Lie bialgebras of the Poisson type are investigated. As by-products,five classes of new infinite-dimensional Lie algebras are obtained.展开更多
Inhomogeneous Oscillator Representations of P(n)Ling Chen Abstract We study inhomogeneous oscillator representations of the strange Lie superalgebras P(n) on supersymmetric polynomial algebras and on spaces of supersy...Inhomogeneous Oscillator Representations of P(n)Ling Chen Abstract We study inhomogeneous oscillator representations of the strange Lie superalgebras P(n) on supersymmetric polynomial algebras and on spaces of supersymmetric exponentialpolynomial functions.We obtain the composition series for these representations.The obtained irreducible modules are infinite dimensional.Some of them are not of highest-weight type and even not weight modules.展开更多
We study inhomogeneous oscillator representations of the strange Lie superalgebras P(n)on supersymmetric polynomial algebras and on spaces of supersymmetric exponential-polynomial functions.We obtain the composition s...We study inhomogeneous oscillator representations of the strange Lie superalgebras P(n)on supersymmetric polynomial algebras and on spaces of supersymmetric exponential-polynomial functions.We obtain the composition series for these representations.The obtained irreducible modules are infinite dimensional.Some of them are not of highest-weight type and even not weight modules.展开更多
The coordinate ring O_(q)(K^(n))of quantum affine space is the K-algebra presented by generators x_(1),...,x_(n) and relations x_(i)x_(j)=q_(ij)a_(j)a_(i) for all i,j.We construct simple O_(q)(K^(n))-modules in a more...The coordinate ring O_(q)(K^(n))of quantum affine space is the K-algebra presented by generators x_(1),...,x_(n) and relations x_(i)x_(j)=q_(ij)a_(j)a_(i) for all i,j.We construct simple O_(q)(K^(n))-modules in a more general setting where the parameters qij lie in a torsion subgroup of K^(*)and show that analogous results hold as in the uniparameter case.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No.10975075Program for New Century Excellent Talents in University,and the Project-sponsored 5 by SRF for ROCS,SEM
文摘The polynomial algebra is a deformed su（2） algebra. Here, we use polynomial algebra az a method to solve a series of deformed oscillators. Thus, we find a series of physics systems corresponding with polynomial algebra with different highest orders.
文摘The filtered-graded transfer of SAGBI bases computation in solvable polynomial algebras was considered. The relations among the SAGBI bases of a subalgebra B, its associated graded algebra G(B) and Rees algebra B were got. These relations solve a natural question: how to determine the generating set of G(B) and B from any given generating set of B. Based on these some equivalent conditions for the existence of finite SAGBI bases can be got.
文摘In this study, particular matrices which is called P-matrices were defined for the action of the Steenrod powers on the polynomial algebra and it was shown that they can be used to calculate the action of Steenrod powers on product of two generators. Finally an algorithm was given to obtain these matrices.
基金the National Natural Science Foundation of China (10371036)the Natural Science Foundation of Beijing (1042001)the Fundamental Research Foundation of Beijing University of Technology (KZ0601200382)
文摘This paper deals with Δ-good filtration dimensions of a standardly stratified algebra and Δ[x]-good titration dimensions of its polynomial algebra.
文摘Let P-n be an algebraic polynomial of degree n with real coefficients. We study the extremal properties of the integral integral(-1)(1)(P ''(n) (x))(2)dx and integral(-1)(1) (1-x(2))1/2(P ''(n)(x))(2)dx subject to the constraint max \P-n(x)\less than or equal to 1.
基金Supported by Guangdong Province Innovation Talent Project for Youths(Grant No.2015KQNCX107)Guangdong University of Education Special Fund for Doctoral Research(Grant No.2016ARF06)
文摘Framed links in thickened torus is studied. We give an expression of torus knot in the Kauffman bracket skein algebra. From this expression and using the theory of Gr？bner bases, we drive the reduced polynomial of a framed link, which is an ambient isotopic invariant and can be computed feasibly.
文摘An enhaned NTRU cryptosystem eliminating decryption failures is proposed without using padding schemes and can resist the oracle model andchosen-ciphertext attacks. Because lattice reduction is the main threat to lattice-based cryptosystems, lattice reductionalgorithms are analyzed to evaluate the security of this scheme. Furthermore, the new scheme remains the advantage of high efficiency of original NTRU.
基金Supported by National Key R&D Program of China(Grant No.2020YFA0712600)。
文摘In our earlier paper,we generalize the one-parameter(c)family of inhomogeneous firstorder differential operator representations of the orthogonal Lie algebras arising from conformal transformations to those of orthosymplectic Lie super algebras,and determine the irreducible condition.This paper deals with the cases when the irreducible condition fails.We prove that if n-m-1>0 and c is an integer satisfying 1≤c≤n-m-1,the representation of osp(2n+2|2m)has a composition series of length 2,and when n-m-1≥0 and c∈-N,the representation of osp(2n+2|2m)has a composition series of length 3,where N is the set of nonnegative integers.Moreover,we show that if c∈(max{n-m,0}-1/2-N)∪(-N),the representation of osp(2n+3|2m)has a composition series of length 2.In particular,we obtain an explicit presentation of the irreducible module with highest weight lλ2-λ1,where l is any positive integer and it is not a generalized Verma module.
基金supported by National Natural Science Foundation of China(Grant Nos.11071147,11431010 and 11371278)Natural Science Foundation of Shandong Province(Grant Nos.ZR2010AM003and ZR2013AL013)+1 种基金Shanghai Municipal Science and Technology Commission(Grant No.12XD1405000)Fundamental Research Funds for the Central Universities
文摘Let A = F [x, y] be the polynomial algebra on two variables x, y over an algebraically closed field F of characteristic zero. Under the Poisson bracket, A is equipped with a natural Lie algebra structure. It is proven that the maximal good subspace of A* induced from the multiplication of the associative commutative algebra A coincides with the maximal good subspace of A* induced from the Poisson bracket of the Poisson Lie algebra A. Based on this, structures of dual Lie bialgebras of the Poisson type are investigated. As by-products,five classes of new infinite-dimensional Lie algebras are obtained.
文摘Inhomogeneous Oscillator Representations of P(n)Ling Chen Abstract We study inhomogeneous oscillator representations of the strange Lie superalgebras P(n) on supersymmetric polynomial algebras and on spaces of supersymmetric exponentialpolynomial functions.We obtain the composition series for these representations.The obtained irreducible modules are infinite dimensional.Some of them are not of highest-weight type and even not weight modules.
基金Supported by the Fundamental Research Funds for the Central Universities,NSFC(Grant No.11401559)UCAS(Grant No.Y55202HY00)。
文摘We study inhomogeneous oscillator representations of the strange Lie superalgebras P(n)on supersymmetric polynomial algebras and on spaces of supersymmetric exponential-polynomial functions.We obtain the composition series for these representations.The obtained irreducible modules are infinite dimensional.Some of them are not of highest-weight type and even not weight modules.
文摘The coordinate ring O_(q)(K^(n))of quantum affine space is the K-algebra presented by generators x_(1),...,x_(n) and relations x_(i)x_(j)=q_(ij)a_(j)a_(i) for all i,j.We construct simple O_(q)(K^(n))-modules in a more general setting where the parameters qij lie in a torsion subgroup of K^(*)and show that analogous results hold as in the uniparameter case.
