Using the theory of derivations on finitely generated and graded Lie algebras, we determine that derivations of the BMS-Weyl algebra are all inner. On this basis, it is proved that every 2-local derivation of the BMS-...Using the theory of derivations on finitely generated and graded Lie algebras, we determine that derivations of the BMS-Weyl algebra are all inner. On this basis, it is proved that every 2-local derivation of the BMS-Weyl algebra is a derivation.展开更多
Let M be a full Hilbert C*-module over a C*-algebra A, and let End^(.A4) be the algebra of adjointable operators on M. We show that if A is unital and commutative, then every derivation of End*A(M) is an inner ...Let M be a full Hilbert C*-module over a C*-algebra A, and let End^(.A4) be the algebra of adjointable operators on M. We show that if A is unital and commutative, then every derivation of End*A(M) is an inner derivation, and that if A is a-unital and commutative, then innerness of derivations on "compact" operators completely decides innerness of derivations on EndA(M). If .4 is unital (no commutativity is assumed) such that every derivation of A is inner, then it is proved that every derivation of EndA(Ln(A)) is also inner, where Ln(A) denotes the direct sum of n copies of A. In addition, in case A is unital, commutative and there exist xo,yo ∈M such that 〈xo,yo〉 = 1, we characterize the linear A-module homomorphisms on EndA(M) which behave like derivations when acting on zero products.展开更多
A scattered operator is a bounded linear operator with at most countable spectrum.In this paper,we prove that for any elementary operator on B(H),not only for finite length but also for infinite length,if the range of...A scattered operator is a bounded linear operator with at most countable spectrum.In this paper,we prove that for any elementary operator on B(H),not only for finite length but also for infinite length,if the range of the elementary operator is contained in scattered operators,then the corresponding sum of multipliers is a compact operator.We also prove that for some special classes of elementary operators,such as the elementary operators of length 2,higher order inner derivations and generalized inner derivation,if the range of the elementary operator is contained in the set of scattered operators,then the range is contained in the set of power compact operators.At the same time,the multipliers of the corresponding elementary operators are characterized.展开更多
Let g be an n-Lie superalgebra. We study the double derivation algebra 7)(g) and describe the relation between 7)(9) and the usual derivation Lie superalgebra Der(9). We show that the set 7)(9) of all doubl...Let g be an n-Lie superalgebra. We study the double derivation algebra 7)(g) and describe the relation between 7)(9) and the usual derivation Lie superalgebra Der(9). We show that the set 7)(9) of all double derivations is a subalgebra of the general linear Lie superalgebra gl(9) and the inner derivation algebra ad(9) is an ideal of 7)(9). We also show that if 9 is a perfect n-Lie superalgebra with certain constraints on the base field, then the centralizer of ad(9) in 7P(9) is trivial. Finally, we give that for every perfect n-Lie superalgebra 9, the triple derivations of the derivation algebra Der(9) are exactly the derivations of Der(9).展开更多
We construct two kinds of infinite-dimensional 3-Lie algebras from a given commutative associative algebra, and show that they are all canonical Nambu 3-Lie algebras. We relate their inner derivation algebras to Witt ...We construct two kinds of infinite-dimensional 3-Lie algebras from a given commutative associative algebra, and show that they are all canonical Nambu 3-Lie algebras. We relate their inner derivation algebras to Witt algebras, and then study the regular representations of these 3-Lie algebras and the natural representations of the inner derivation algebras. In particular, for the second kind of 3-Lie algebras, we find that their regular representations are Harish-Chandra modules, and the inner derivation algebras give rise to intermediate series modules of the Witt algebras and contain the smallest full toroidal Lie algebras without center.展开更多
Let F be a field of characteristic 0, Mn(F) the full matrix algebra over F, t the subalgebra of Mn(F) consisting of all upper triangular matrices. Any subalgebra of Mn(F) containing t is called a parabolic subal...Let F be a field of characteristic 0, Mn(F) the full matrix algebra over F, t the subalgebra of Mn(F) consisting of all upper triangular matrices. Any subalgebra of Mn(F) containing t is called a parabolic subalgebra of Mn(F). Let P be a parabolic subalgebra of Mn(F). A map φ on P is said to satisfy derivability if φ(x·y) = φ(x)·y+x·φ(y) for all x,y ∈ P, where φ is not necessarily linear. Note that a map satisfying derivability on P is not necessarily a derivation on P. In this paper, we prove that a map φ on P satisfies derivability if and only if φ is a sum of an inner derivation and an additive quasi-derivation on P. In particular, any derivation of parabolic subalgebras of Mn(F) is an inner derivation.展开更多
基金National Natural Science Foundation of China(11971315)。
文摘Using the theory of derivations on finitely generated and graded Lie algebras, we determine that derivations of the BMS-Weyl algebra are all inner. On this basis, it is proved that every 2-local derivation of the BMS-Weyl algebra is a derivation.
基金supported by National Natural Science Foundation of China(Grant No.11171151)Natural Science Foundation of Jiangsu Province of China(Grant No.BK2011720)supported by Singapore Ministry of Education Academic Research Fund Tier1(Grant No.R-146-000-136-112)
文摘Let M be a full Hilbert C*-module over a C*-algebra A, and let End^(.A4) be the algebra of adjointable operators on M. We show that if A is unital and commutative, then every derivation of End*A(M) is an inner derivation, and that if A is a-unital and commutative, then innerness of derivations on "compact" operators completely decides innerness of derivations on EndA(M). If .4 is unital (no commutativity is assumed) such that every derivation of A is inner, then it is proved that every derivation of EndA(Ln(A)) is also inner, where Ln(A) denotes the direct sum of n copies of A. In addition, in case A is unital, commutative and there exist xo,yo ∈M such that 〈xo,yo〉 = 1, we characterize the linear A-module homomorphisms on EndA(M) which behave like derivations when acting on zero products.
基金Supported by National Natural Science Foundation of China(Grant No.12071029)。
文摘A scattered operator is a bounded linear operator with at most countable spectrum.In this paper,we prove that for any elementary operator on B(H),not only for finite length but also for infinite length,if the range of the elementary operator is contained in scattered operators,then the corresponding sum of multipliers is a compact operator.We also prove that for some special classes of elementary operators,such as the elementary operators of length 2,higher order inner derivations and generalized inner derivation,if the range of the elementary operator is contained in the set of scattered operators,then the range is contained in the set of power compact operators.At the same time,the multipliers of the corresponding elementary operators are characterized.
文摘Let g be an n-Lie superalgebra. We study the double derivation algebra 7)(g) and describe the relation between 7)(9) and the usual derivation Lie superalgebra Der(9). We show that the set 7)(9) of all double derivations is a subalgebra of the general linear Lie superalgebra gl(9) and the inner derivation algebra ad(9) is an ideal of 7)(9). We also show that if 9 is a perfect n-Lie superalgebra with certain constraints on the base field, then the centralizer of ad(9) in 7P(9) is trivial. Finally, we give that for every perfect n-Lie superalgebra 9, the triple derivations of the derivation algebra Der(9) are exactly the derivations of Der(9).
基金This work was supported in part by the National Natural Science Foundation of China (Grant No. 11371245) and the Natural Science Foundation of Hebei Province, China (Grant No. A2014201006).
文摘We construct two kinds of infinite-dimensional 3-Lie algebras from a given commutative associative algebra, and show that they are all canonical Nambu 3-Lie algebras. We relate their inner derivation algebras to Witt algebras, and then study the regular representations of these 3-Lie algebras and the natural representations of the inner derivation algebras. In particular, for the second kind of 3-Lie algebras, we find that their regular representations are Harish-Chandra modules, and the inner derivation algebras give rise to intermediate series modules of the Witt algebras and contain the smallest full toroidal Lie algebras without center.
基金Supported by the National Natural Science Foundation of China (Grant No.11071040)the Natural Science Foundation of Fujian Province (Grant No. 2009J05005)
文摘Let F be a field of characteristic 0, Mn(F) the full matrix algebra over F, t the subalgebra of Mn(F) consisting of all upper triangular matrices. Any subalgebra of Mn(F) containing t is called a parabolic subalgebra of Mn(F). Let P be a parabolic subalgebra of Mn(F). A map φ on P is said to satisfy derivability if φ(x·y) = φ(x)·y+x·φ(y) for all x,y ∈ P, where φ is not necessarily linear. Note that a map satisfying derivability on P is not necessarily a derivation on P. In this paper, we prove that a map φ on P satisfies derivability if and only if φ is a sum of an inner derivation and an additive quasi-derivation on P. In particular, any derivation of parabolic subalgebras of Mn(F) is an inner derivation.