Deformed Kac-Moody Algebra and Noncommutative Fermi Theory in Two-Dimensions

Abstract

Starting from noncommutative Fermi theory in two-dimensions, we construct a deformed Kac-Moody algebra between its vector and Chiral currents . The higher-order corrections to the deformed Kac-Moody algebra are explicitly calculated. We observe that the ordinary Schwinger terms are not affected by noncommutativity. Finally we conclude that the deformed Kac-Moody algebra can be given in term of ordinary Kac-Moody algebra plus infinitely many Lie algebraic structures at each non-zero power of the antisymmetric coefficient $\theta$.

13 pages

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Cited by in corpus (1)

• Integral Transforms and $\mathcal{P}\mathcal{T}$-symmetric Hamiltonians