The variety ddpM of de Morgan algebras with double demi-pseudocomplementation consists of those algebras （L; ∧ , ∨ , , , ＋ , 0, 1） of type （2, 2, 1, 1, 1, 0, 0） where （L; ∧ , ∨ , , 0, 1） is a de Morgan alge...The variety ddpM of de Morgan algebras with double demi-pseudocomplementation consists of those algebras （L; ∧ , ∨ , , , ＋ , 0, 1） of type （2, 2, 1, 1, 1, 0, 0） where （L; ∧ , ∨ , , 0, 1） is a de Morgan algebra, （L; ∧ , ∨ , , ＋ , 0, 1） is a double demi-p-lattice and the operations x → x , x → x and x → x ＋ are linked by the identities x = x , x ＋ = x ＋ and x ＋ = x ＋ . In this paper, we characterize congruences on a ddpM-algebra, and give a description of the subdirectly irreducible algebras.展开更多
Some equivalent conditions for double Frobenius algebras to be strict ones are given. Then some examples of （strict or non-strict） double Frobenius algebras are presented. Finally, a sufficient and necessary conditi...Some equivalent conditions for double Frobenius algebras to be strict ones are given. Then some examples of （strict or non-strict） double Frobenius algebras are presented. Finally, a sufficient and necessary condition for the trivial extension of a double Frobenius algebra to be a （strict） double Frobenius algebra is given.展开更多
In the Ringel-Hall algebra of Dynkin type,the set of all commutator relations between the isoclasses of indecomposable representations forms a minimal Grobner-Shirshov basis and the set of the corresponding irreducibl...In the Ringel-Hall algebra of Dynkin type,the set of all commutator relations between the isoclasses of indecomposable representations forms a minimal Grobner-Shirshov basis and the set of the corresponding irreducible elements forms a PBW-type basis of the Ringel-Hall algebra.We aim to generalize this result to the reduced Drinfeld double Hall algebra of type A_(n).First,we compute a minimal Grobner-Shirshov basis for the reduced Drinfeld double Hall algebra of type An by proving that all possible compositions between the commutator relations are trivial.Then,by taking the corresponding irreducible monomials,we construct a PBW-type basis for the reduced Drinfeld double Hall algebra of type A_(n).展开更多
In this paper,we study a certain class of double Ockham algebras(L;∧,∨,f,k,0,1),namely the bounded distributive lattices(L;∧,∨,0,1)endowed with a commuting pair of unary op-erations f and k,both of which are dual ...In this paper,we study a certain class of double Ockham algebras(L;∧,∨,f,k,0,1),namely the bounded distributive lattices(L;∧,∨,0,1)endowed with a commuting pair of unary op-erations f and k,both of which are dual endomorphisms.We characterize the subdirectly irreducible members,and also consider the special case when both(L;f)and(L;k)are de Morgan algebras.We show via Priestley duality that there are precisely nine non-isomorphic subdirectly irreducible members,all of which are simple.展开更多
We introduce the doubled Hecke algebra,which is an infinite-dimensional algebra generated by two Hecke algebras.This concept originates from the degenerate doubled Hecke algebra in the theory of Schur-Weyl duality rel...We introduce the doubled Hecke algebra,which is an infinite-dimensional algebra generated by two Hecke algebras.This concept originates from the degenerate doubled Hecke algebra in the theory of Schur-Weyl duality related to enhanced reductive algebraic groups.We study the finite-dimensional natural representation of the doubled Hecke algebra on tensor space and prove that the doubled Hecke algebra forms a duality with the quantum group of Levi type.展开更多
Imaginary Verma modules, parabolic imaginary Verma modules, and Verma modules at level zero for double affine Lie algebras are constructed using three different triangular decompositions. Their relations are investiga...Imaginary Verma modules, parabolic imaginary Verma modules, and Verma modules at level zero for double affine Lie algebras are constructed using three different triangular decompositions. Their relations are investigated, and several results are generalized from the affine Lie algebras. In particular, imaginary highest weight modules, integrable modules, and irreducibility criterion are also studied.展开更多
This paper gives a complete classification of (Δ)-finite twisted double incidence algebras of posets in the case where the Hasse quivers of posets are of type An.
Let A be an arbitrary hereditary abelian category. Lu and Peng (2021) defined the semi-derived Ringel-Hall algebra SDH(A) of A and proved that SDH(A) has a natural basis and is isomorphic to the Drinfeld double Ringel...Let A be an arbitrary hereditary abelian category. Lu and Peng (2021) defined the semi-derived Ringel-Hall algebra SDH(A) of A and proved that SDH(A) has a natural basis and is isomorphic to the Drinfeld double Ringel-Hall algebra of A. In this paper, we introduce a coproduct formula on SDH(A) with respect to the basis of SDH(A) and prove that this coproduct is compatible with the product of SDH(A), and thereby the semi-derived Ringel-Hall algebra of A is endowed with a bialgebra structure which is identified with the bialgebra structure of the Drinfeld double Ringel-Hall algebra of A.展开更多
Suppose that G is a finite group and D（G） the double algebra of G. For a given subgroup H of G, there is a sub-Hopf algebra D（G; H） of D（G）. This paper gives the concrete construction of a D（G; H）-invariant su...Suppose that G is a finite group and D（G） the double algebra of G. For a given subgroup H of G, there is a sub-Hopf algebra D（G; H） of D（G）. This paper gives the concrete construction of a D（G; H）-invariant subspace AH in field algebra of G-spin model and proves that if H is a normal subgroup of G, then AH is Galois closed.展开更多
A useful reduction is presented to determine the finiteness of Δ -good module category F(Δ) of a quasi-hereditary algebra.As an application of the reduction, the F(Δ) -finiteness of quasihereditary M-twis...A useful reduction is presented to determine the finiteness of Δ -good module category F(Δ) of a quasi-hereditary algebra.As an application of the reduction, the F(Δ) -finiteness of quasihereditary M-twisted double incidence algebras of posets is discussed. In particular, a complete classification of F(Δ)- finite M-twisted double incidence algebras is given in case the posets are linearly ordered.展开更多
文摘The variety ddpM of de Morgan algebras with double demi-pseudocomplementation consists of those algebras （L; ∧ , ∨ , , , ＋ , 0, 1） of type （2, 2, 1, 1, 1, 0, 0） where （L; ∧ , ∨ , , 0, 1） is a de Morgan algebra, （L; ∧ , ∨ , , ＋ , 0, 1） is a double demi-p-lattice and the operations x → x , x → x and x → x ＋ are linked by the identities x = x , x ＋ = x ＋ and x ＋ = x ＋ . In this paper, we characterize congruences on a ddpM-algebra, and give a description of the subdirectly irreducible algebras.
基金This work was supported by the National Natural Science Foundation of China （Grant No. 11471282）, the China Postdoctoral Science Foundation （Grant No. 2017M610316）, and the Natural Science Foundation of Jiangsu Province （Grant No. BK20170589）.
文摘Some equivalent conditions for double Frobenius algebras to be strict ones are given. Then some examples of （strict or non-strict） double Frobenius algebras are presented. Finally, a sufficient and necessary condition for the trivial extension of a double Frobenius algebra to be a （strict） double Frobenius algebra is given.
基金Supported by National Natural Science Foundation of China(Grant No.11861061).
文摘In the Ringel-Hall algebra of Dynkin type,the set of all commutator relations between the isoclasses of indecomposable representations forms a minimal Grobner-Shirshov basis and the set of the corresponding irreducible elements forms a PBW-type basis of the Ringel-Hall algebra.We aim to generalize this result to the reduced Drinfeld double Hall algebra of type A_(n).First,we compute a minimal Grobner-Shirshov basis for the reduced Drinfeld double Hall algebra of type An by proving that all possible compositions between the commutator relations are trivial.Then,by taking the corresponding irreducible monomials,we construct a PBW-type basis for the reduced Drinfeld double Hall algebra of type A_(n).
文摘In this paper,we study a certain class of double Ockham algebras(L;∧,∨,f,k,0,1),namely the bounded distributive lattices(L;∧,∨,0,1)endowed with a commuting pair of unary op-erations f and k,both of which are dual endomorphisms.We characterize the subdirectly irreducible members,and also consider the special case when both(L;f)and(L;k)are de Morgan algebras.We show via Priestley duality that there are precisely nine non-isomorphic subdirectly irreducible members,all of which are simple.
基金supported by the National Natural Science Foundation of China(NSFC)Grant 12071136.
文摘We introduce the doubled Hecke algebra,which is an infinite-dimensional algebra generated by two Hecke algebras.This concept originates from the degenerate doubled Hecke algebra in the theory of Schur-Weyl duality related to enhanced reductive algebraic groups.We study the finite-dimensional natural representation of the doubled Hecke algebra on tensor space and prove that the doubled Hecke algebra forms a duality with the quantum group of Levi type.
基金N. Jing＇s work was partially supported by the Simons Foundation （Grant No. 198129） and the National Natural Science Foundation of China （Grant No. 11271138）, and he also acknowledged the hospitality of Max-Planck Institute for Mathematics in the Sciences at Leipzig during this work.
文摘Imaginary Verma modules, parabolic imaginary Verma modules, and Verma modules at level zero for double affine Lie algebras are constructed using three different triangular decompositions. Their relations are investigated, and several results are generalized from the affine Lie algebras. In particular, imaginary highest weight modules, integrable modules, and irreducibility criterion are also studied.
文摘This paper gives a complete classification of (Δ)-finite twisted double incidence algebras of posets in the case where the Hasse quivers of posets are of type An.
文摘Let A be an arbitrary hereditary abelian category. Lu and Peng (2021) defined the semi-derived Ringel-Hall algebra SDH(A) of A and proved that SDH(A) has a natural basis and is isomorphic to the Drinfeld double Ringel-Hall algebra of A. In this paper, we introduce a coproduct formula on SDH(A) with respect to the basis of SDH(A) and prove that this coproduct is compatible with the product of SDH(A), and thereby the semi-derived Ringel-Hall algebra of A is endowed with a bialgebra structure which is identified with the bialgebra structure of the Drinfeld double Ringel-Hall algebra of A.
基金supported by National Science Foundation of China(10301004)
文摘Suppose that G is a finite group and D（G） the double algebra of G. For a given subgroup H of G, there is a sub-Hopf algebra D（G; H） of D（G）. This paper gives the concrete construction of a D（G; H）-invariant subspace AH in field algebra of G-spin model and proves that if H is a normal subgroup of G, then AH is Galois closed.
文摘A useful reduction is presented to determine the finiteness of Δ -good module category F(Δ) of a quasi-hereditary algebra.As an application of the reduction, the F(Δ) -finiteness of quasihereditary M-twisted double incidence algebras of posets is discussed. In particular, a complete classification of F(Δ)- finite M-twisted double incidence algebras is given in case the posets are linearly ordered.
