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arXiv:1505.01516

On quantum Freidel-Maillet algebra for non-ultralocal integrable systems

A. Melikyan, G. Weber

Published May 6, 2015• 0 citations
arXivHTMLPDF

Abstract

We consider the quantum algebra of transition matrices for non-ultralocal integrable systems, and show that a regularization of the singular operator products in the quantum algebra via Sklyanin's product leads to well-defined expressions, reproducing in the classical limit Maillet's symmetrization prescription for Poisson brackets.

DOI
10.48550/arxiv.1505.01516

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We consider the quantum algebra of transition matrices for non-ultralocal integrable systems, and show that a regularization of the singular operator products in the quantum algebra via Sklyanin's product leads to well-defined expressions, reproducing in the classical limit Maillet's symmetrization prescription for Poisson brackets.
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A scheme suitable for describing quantum non-ultralocal models, including supersymmetric ones, is proposed. Braided algebras are generalized to be used through Baxterization for constructing braided quantum Yang—Baxter equations. Supersymmetric and some known non-ultralocal models are derived in the framework of this approach. As further applications of the scheme, the construction of new quantum integrable non-ultralocal models, like mKdV and anyonic supersymmetric models including deformed anyonic superalgebra, is outlined.
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