1998arXiv (Cornell University)Open access

Generalized quantum current algebras

Liu Zhao

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Abstract

Two general families of new quantum deformed current algebras are proposed and identified both as infinite Hopf family of algebras, a structure which enable one to define ``tensor products'' of these algebras. The standard quantum affine algebras turn out to be a very special case of both algebra families, in which case the infinite Hopf family structure degenerates into standard Hopf algebras. The relationship between the two algebra families as well as their various special examples are discussed, and the free boson representation is also considered.

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Two general families of new quantum deformed current algebras are proposed and identified both as infinite Hopf family of algebras, a structure which enable one to define ``tensor products'' of these algebras. The standard quantum affine algebras turn out to be a very special case of both algebra families, in which case the infinite Hopf family structure degenerates into standard Hopf algebras. The relationship between the two algebra families as well as their various special examples are discussed, and the free boson representation is also considered.

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Available abstract

Two general families of new quantum deformed current algebras are proposed and identified both as infinite Hopf family of algebras, a structure which enable one to define ``tensor products'' of these algebras. The standard quantum affine algebras turn out to be a very special case of both algebra families, in which case the infinite Hopf family structure degenerates into standard Hopf algebras. The relationship between the two algebra families as well as their various special examples are discussed, and the free boson representation is also considered.

Key concepts: Current (fluid), Quantum, Theoretical physics, Pure mathematics, Political science, Physics, Mathematics, Quantum mechanics

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