New Generalized Simple Lie Algebras of Cartan Type over a Field with Characteristic 0

Xu, Xiaoping

doi:10.1006/jabr.1998.8083

Cited by 74 publications

(63 citation statements)

References 14 publications

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“…Thus by Su et al (2000), we see that the structure space of the (associative or Lie) algebras of Weyl type in (1.7) is the same as that of simple Lie algebras of generalized Witt type constructed in Xu (2000).…”

Section: In Other Words the Set Sw Is The Structure Space Of The (Asmentioning

confidence: 56%

Structure of Algebras of Weyl Type

Zhao

2004

Communications in Algebra

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In a recent paper by the authors, the associative and the Lie algebras of Weyl typewere introduced, where A is a commutative associative algebra with an identity element over a field F of any characteristic, and F[D] is the polynomial algebra of a commutative derivation subalgebra D of A. In the present paper, a class of the above associative and Lie algebras A[D] with F being a field of characteristic 0 and D consisting of locally finite derivations of A, is studied. The isomorphism classes of these associative and Lie algebras are determined. The structure of these algebras is described explicitly.

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Section: In Other Words the Set Sw Is The Structure Space Of The (Asmentioning

confidence: 56%

Structure of Algebras of Weyl Type

Zhao

2004

Communications in Algebra

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“…(29) can only take values in odd numbers, the algebra is a subalgebra of the Lie algebra considered in [16], which is a Block type Lie algebra as well as a special case of Hamiltonian type Lie algebras (see, e.g., [20,21]). The above results together with that on [19] …”

Section: Proofmentioning

confidence: 99%

Block (or Hamiltonian) Lie Symmetry of Dispersionless D-Type Drinfeld–Sokolov Hierarchy

2014

Commun. Theor. Phys.

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“…for a, b, c ∈ G. Denote by A 1 = A(G, E, f ) the (ǫ, Γ)-color commutative associative algebra with E-basis {x a | a ∈ G} or E 0 -basis {E α x a | (α, a) ∈ Γ 0 × G} such that x a has color a and 12) and in general …”

Section: D-simple Color Algebrasmentioning

confidence: 99%

Classification of derivation-simple color algebras related to locally finite derivations

Zhao

Zhu

2003

Journal of Mathematical Physics

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We classify the pairs (A, D) consisting of an (ǫ, Γ)-color-commutative associative algebra A with an identity element over an algebraically closed field F of characteristic zero and a finite dimensional subspace D of (ǫ, Γ)-color-commutative locally finite color-derivations of A such that A is Γ-graded D-simple and the eigenspaces for elements of D are Γ-graded. Such pairs are the important ingredients in constructing some simple Lie color algebras which are in general not finitely-graded. As some applications, using such pairs, we construct new explicit simple Lie color algebras of generalized Witt type, Weyl type.

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New Generalized Simple Lie Algebras of Cartan Type over a Field with Characteristic 0

Abstract: We construct four new series of generalized simple Lie algebras of Cartan type, using the mixtures of grading operators and down-grading operators. Our results in this paper are further generalizations of those in Osborn's work (J. Algebra 185 (1996), 820-835).

Cited by 74 publications

References 14 publications

Structure of Algebras of Weyl Type

Structure of Algebras of Weyl Type

Block (or Hamiltonian) Lie Symmetry of Dispersionless D-Type Drinfeld–Sokolov Hierarchy

Classification of derivation-simple color algebras related to locally finite derivations

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