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1994•Journal of Mathematical PhysicsRequires access

q-deformation of high-order Virasoro algebra

Chao-Zheng Zha

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Abstract

The high-order Virasoro algebra (HOVA) is deformed on a quantum plane C2‖0 in a formalism reducible to the ordinary HOVA when q→1. After introducing the ‘‘associator,’’ the Jacobi identity and central extensions are also investigated. The q-deformed HOVA possesses a Hopf algebra structure within the framework of q-product algebra. The W∞-algebra expressed in terms of linear combinations of HOVA can thus be q-deformed and possess a Hopf algebra structure.

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What this paper is about

The high-order Virasoro algebra (HOVA) is deformed on a quantum plane C2‖0 in a formalism reducible to the ordinary HOVA when q→1. After introducing the ‘‘associator,’’ the Jacobi identity and central extensions are also investigated. The q-deformed HOVA possesses a Hopf algebra structure within the framework of q-product algebra. The W∞-algebra expressed in terms of linear combinations of HOVA can thus be q-deformed and possess a Hopf algebra structure.

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Available abstract

The high-order Virasoro algebra (HOVA) is deformed on a quantum plane C2‖0 in a formalism reducible to the ordinary HOVA when q→1. After introducing the ‘‘associator,’’ the Jacobi identity and central extensions are also investigated. The q-deformed HOVA possesses a Hopf algebra structure within the framework of q-product algebra. The W∞-algebra expressed in terms of linear combinations of HOVA can thus be q-deformed and possess a Hopf algebra structure.

Key concepts: Filtered algebra, Virasoro algebra, Cellular algebra, Hopf algebra, Current algebra, Algebra over a field, Algebra representation, Quantum affine algebra

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