Drinfeld Yangian of the queer Lie superalgebra. I

TL;DR

This paper defines the Drinfeld Yangian for the queer Lie superalgebra as a quantization of a twisted polynomial current Lie bisuperalgebra, constructing a new generator system and proving isomorphism with Nazarov's Yangian in a special case.

Contribution

It introduces a new construction of the Drinfeld Yangian for the queer Lie superalgebra and proves its equivalence to Nazarov's Yangian in a specific instance.

Findings

Construction of the Drinfeld Yangian for the queer Lie superalgebra.

Development of a new generator system for this Yangian.

Proof of isomorphism with Nazarov's Yangian for the case of $sq_1$.

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 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.