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Bibliographic Details
Main Authors: Panasyuk, Andriy, Skrypnyk, Taras
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2509.24054
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Table of Contents:
  • In the present paper, using two constant tensors $c$ and $b$ on $sl(N)\otimes sl(N)$ satisfying certain linear-quadratic equation and a technique of Poisson bivectors and Schouten brackets, we explicitly construct quadratic Poisson bracket on the space $ (sl(N)+\mathbb{C})^*$ which is compatible with the standard Lie--Poisson bracket on $gl(N)^* \simeq (sl(N)\oplus \mathbb{C})^*$. The case of $N=3$ is considered in details. The relation of the proposed brackets with the generalized classical Sklyanin algebras is explained.