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2020•Lobachevskii Journal of MathematicsRequires access

The Drinfeld Yangian of the Queer Lie Superalgebra. Defining Relations

Vladimir Alekseevich Stukopin

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Abstract

Abstract Drinfeld Yangian of a queer Lie superalgebra is defined as the quantization of a Lie bisuperelgebra of twisted polynomial currents. An analogue of the new system of generators of Drinfeld is being constructed. It is proved for the partial case of Lie superalgebra $$sq_{1}$$ that this so defined Yangian and the Yangian, introduced earlier by M. Nazarov using the Faddeev–Reshetikhin–Takhtadzhjan approach, are isomorphic.

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Abstract Drinfeld Yangian of a queer Lie superalgebra is defined as the quantization of a Lie bisuperelgebra of twisted polynomial currents. An analogue of the new system of generators of Drinfeld is being constructed. It is proved for the partial case of Lie superalgebra $$sq_{1}$$ that this so defined Yangian and the Yangian, introduced earlier by M. Nazarov using the Faddeev–Reshetikhin–Takhtadzhjan approach, are isomorphic.

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Available abstract

Abstract Drinfeld Yangian of a queer Lie superalgebra is defined as the quantization of a Lie bisuperelgebra of twisted polynomial currents. An analogue of the new system of generators of Drinfeld is being constructed. It is proved for the partial case of Lie superalgebra $$sq_{1}$$ that this so defined Yangian and the Yangian, introduced earlier by M. Nazarov using the Faddeev–Reshetikhin–Takhtadzhjan approach, are isomorphic.

Key concepts: Yangian, Lie superalgebra, Mathematics, Supermatrix, Pure mathematics, Queer, Algebra over a field, Superalgebra

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