Let F be a field and char F = p > 3. In this paper the derivation algebras of Lie superalgebras W and S of Cartan-type over F are determined by the calculating method.
A class of the associative and Lie algebras A[D] = A × F[D] of Weyl type are studied, where Ais a commutative associative algebra with an identity element over a field F of characteristic zero, and F[D] isthe pol...A class of the associative and Lie algebras A[D] = A × F[D] of Weyl type are studied, where Ais a commutative associative algebra with an identity element over a field F of characteristic zero, and F[D] isthe polynomial algebra of a finite dimensional commutative subalgebra of locally finite derivations of A suchthat A is D-simple. The derivations of these associative and Lie algebras are precisely determined.展开更多
In this paper, we will prove that every derivation of completely distributive subspace lattice (CDS)algebras on Banach space is automatically continuous. This is new even in the Hilbert space case. As an application o...In this paper, we will prove that every derivation of completely distributive subspace lattice (CDS)algebras on Banach space is automatically continuous. This is new even in the Hilbert space case. As an application of this result, we obtain that every additive derivation of nest algebras on Banach spaces is inner. We will also prove that every isomorphism between nest algebras on Banach space is automatically continuous, and in addition, is spatial.展开更多
Poisson algebras are fundamental algebraic structures in physics and symplectic geometry. However, the structure theory of Poisson algebras has not been well developed. In this paper, we determine the structure of the...Poisson algebras are fundamental algebraic structures in physics and symplectic geometry. However, the structure theory of Poisson algebras has not been well developed. In this paper, we determine the structure of the central simple Poisson algebras related to locally finite derivations, over an algebraically closed field of characteristic zero.The Lie algebra structures of these Poisson algebras are in general not finitely-graded.展开更多
In this paper, we determine the derivation algebra and the automorphism group of the original deformative Schrodinger-Virasoro algebra, which is the semi-direct product Lie algebra of the Witt algebra and its tensor d...In this paper, we determine the derivation algebra and the automorphism group of the original deformative Schrodinger-Virasoro algebra, which is the semi-direct product Lie algebra of the Witt algebra and its tensor density module Ig（a, b）.展开更多
Let A be a subalgebra of B（X） containing the identity operator I and an idempotent P. Suppose that α,β： A →A are ring epimorphisms and there exists some nest N on 2（ such that α（P）（X） and β（P）（X） are ...Let A be a subalgebra of B（X） containing the identity operator I and an idempotent P. Suppose that α,β： A →A are ring epimorphisms and there exists some nest N on 2（ such that α（P）（X） and β（P）（X） are non-trivial elements of N. Let A contain all rank one operators in AlgN and δ ： A→ B（X） be an additive mapping. It is shown that, if δ is （α, β）-derivable at zero point, then there exists an additive （α, β）-derivation τ ： A →β（X） such that δ（A） =τ（A） ＋ α（A）δ（I） for all A∈A. It is also shown that if δ is generalized （α,β）-derivable at zero point, then δ is an additive generalized （α, β）-derivation. Moreover, by use of this result, the additive maps （generalized） （α,β）-derivable at zero point on several nest algebras, are also characterized.展开更多
Invariant symmetric bilinear forms and derivation algebras of a unitary Lie algebra L over R are characterized： （L） ≌ （R＋/（[R, R] A R＋））＊ and Der（L） = Inn（L） ＋ Der（L）0 = Inn（L） ＋ SDer（R）, which ...Invariant symmetric bilinear forms and derivation algebras of a unitary Lie algebra L over R are characterized： （L） ≌ （R＋/（[R, R] A R＋））＊ and Der（L） = Inn（L） ＋ Der（L）0 = Inn（L） ＋ SDer（R）, which recover what of the special linear Lie algebra and Steinberg Lie algebra over R, where R is a unital involutory associative algebra over a field F.展开更多
In this paper, we explicitly determine the maximal torus of the derivation algebra of a Qn filiform Lie algebra. Using the root space decomposition of DerQn, we prove that the derivation algebra of a Qn filiform Lie a...In this paper, we explicitly determine the maximal torus of the derivation algebra of a Qn filiform Lie algebra. Using the root space decomposition of DerQn, we prove that the derivation algebra of a Qn filiform Lie algebra is complete.展开更多
In this paper,we give the notion of derivations of Lie 2-algebras using explicit formulas,and construct the associated derivation Lie 3-algebra.We prove that isomorphism classes of non-abelian extensions of Lie 2-alge...In this paper,we give the notion of derivations of Lie 2-algebras using explicit formulas,and construct the associated derivation Lie 3-algebra.We prove that isomorphism classes of non-abelian extensions of Lie 2-algebras are classified by equivalence classes of morphisms from a Lie 2-algebra to a derivation Lie 3-algebra.展开更多
文摘Let F be a field and char F = p > 3. In this paper the derivation algebras of Lie superalgebras W and S of Cartan-type over F are determined by the calculating method.
基金This work was supported by the Natronal Natural Science Foundation of China(Grant No.10171064)and an EYTP grant of MOE of China.
文摘A class of the associative and Lie algebras A[D] = A × F[D] of Weyl type are studied, where Ais a commutative associative algebra with an identity element over a field F of characteristic zero, and F[D] isthe polynomial algebra of a finite dimensional commutative subalgebra of locally finite derivations of A suchthat A is D-simple. The derivations of these associative and Lie algebras are precisely determined.
文摘In this paper, we will prove that every derivation of completely distributive subspace lattice (CDS)algebras on Banach space is automatically continuous. This is new even in the Hilbert space case. As an application of this result, we obtain that every additive derivation of nest algebras on Banach spaces is inner. We will also prove that every isomorphism between nest algebras on Banach space is automatically continuous, and in addition, is spatial.
基金This work is supported by the National Natural Science Foundation of China (Grant No.10171064)two grants 'Excellent Young Teacher Program' and 'Trans-Century Training Programme Foundation for the Talents' from Ministry of Education of China.
文摘Poisson algebras are fundamental algebraic structures in physics and symplectic geometry. However, the structure theory of Poisson algebras has not been well developed. In this paper, we determine the structure of the central simple Poisson algebras related to locally finite derivations, over an algebraically closed field of characteristic zero.The Lie algebra structures of these Poisson algebras are in general not finitely-graded.
基金This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 10825101, 10861004, 11101266）, SMSTC grant no. 12XD1405000, Fundamental Research Funds for the Central Universities, and Science ＆ Technology Program of Shanghai Maritime University.
文摘We determine the derivation algebra and the automorphism group of the generalized topological N = 2 superconformal algebra.
文摘In this paper, we determine the derivation algebra and the automorphism group of the original deformative Schrodinger-Virasoro algebra, which is the semi-direct product Lie algebra of the Witt algebra and its tensor density module Ig（a, b）.
文摘Let A be a subalgebra of B（X） containing the identity operator I and an idempotent P. Suppose that α,β： A →A are ring epimorphisms and there exists some nest N on 2（ such that α（P）（X） and β（P）（X） are non-trivial elements of N. Let A contain all rank one operators in AlgN and δ ： A→ B（X） be an additive mapping. It is shown that, if δ is （α, β）-derivable at zero point, then there exists an additive （α, β）-derivation τ ： A →β（X） such that δ（A） =τ（A） ＋ α（A）δ（I） for all A∈A. It is also shown that if δ is generalized （α,β）-derivable at zero point, then δ is an additive generalized （α, β）-derivation. Moreover, by use of this result, the additive maps （generalized） （α,β）-derivable at zero point on several nest algebras, are also characterized.
文摘Invariant symmetric bilinear forms and derivation algebras of a unitary Lie algebra L over R are characterized： （L） ≌ （R＋/（[R, R] A R＋））＊ and Der（L） = Inn（L） ＋ Der（L）0 = Inn（L） ＋ SDer（R）, which recover what of the special linear Lie algebra and Steinberg Lie algebra over R, where R is a unital involutory associative algebra over a field F.
文摘In this paper, we explicitly determine the maximal torus of the derivation algebra of a Qn filiform Lie algebra. Using the root space decomposition of DerQn, we prove that the derivation algebra of a Qn filiform Lie algebra is complete.
基金supported by National Natural Science Foundation of China(Grant Nos.11026046,11101179,10971071)Doctoral Fund of Ministry of Education of China(Grant No.20100061120096)the Fundamental Research Funds for the Central Universities(Grant No.200903294)
文摘In this paper,we give the notion of derivations of Lie 2-algebras using explicit formulas,and construct the associated derivation Lie 3-algebra.We prove that isomorphism classes of non-abelian extensions of Lie 2-algebras are classified by equivalence classes of morphisms from a Lie 2-algebra to a derivation Lie 3-algebra.
