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Double Yangian and reflection algebras of the Lie superalgebra $\mathfrak{gl}_{m|n}$

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arxiv 2311.02410 v1 pith:EA2UXI7Z submitted 2023-11-04 math.QA math-phmath.MPmath.RT

Lucia Bagnoli , Slaven Kožić This is my paper · ORCID
classification math.QAmath-phmath.MPmath.RT
keywords doubleyangianalgebrasmathfrakreflectionsuperalgebraapplicationassociated
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abstract

We study the double Yangian associated with the Lie superalgebra $\mathfrak{gl}_{m|n}$. Our main focus is on establishing the Poincar\'{e}-Birkhoff-Witt Theorem for the double Yangian and constructing its central elements in the form of coefficients of the quantum contraction. Next, as an application, we introduce reflection algebras, certain left coideal subalgebras of the level 0 double Yangian, and find their presentations by generators and relations.

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  1. Double Yangian and reflection algebras of the Lie superalgebra $\mathfrak{gl}_{M|N}$, II: Quantum currents

    math.QA 2026-08 conditional novelty 6.0 of 10

    The authors extend the Etingof-Kazhdan quantum vertex algebra construction and the critical-level central element construction from the double Yangian of gl_M to the Lie superalgebra gl_{M|N}.

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