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.
Double Yangian and reflection algebras of the Lie superalgebra $\mathfrak{gl}_{m|n}$ / Bagnoli, L., Kožić, S.. - In: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. - ISSN 1793-6683. - 27:(2025). [10.1142/S021919972450007X]
Double Yangian and reflection algebras of the Lie superalgebra $\mathfrak{gl}_{m|n}$
Bagnoli, Lucia;
2025
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.| File | Dimensione | Formato | |
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