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arXiv · 2311.02410

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

Lucia Bagnoli·Slaven Kožić
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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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BibTeXRIS

Lucia Bagnoli, Slaven Kožić. 2023-11-04. Double Yangian and reflection algebras of the Lie superalgebra $\mathfrak{gl}_{m|n}$. https://doi.org/10.1142/s021919972450007x

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