W -algebras via Lax type operators

Valeri, D. (2021) W -algebras via Lax type operators. In: Paranjape, M.B., MacKenzie, R., Thomova, Z., Winternitz, P. and Witczak-Krempa, W. (eds.) Quantum Theory and Symmetries: Proceedings of the 11th International Symposium, Montreal, Canada. Series: CRM series in mathematical physics. Springer: Cham, pp. 181-198. ISBN 9783030557768 (doi: 10.1007/978-3-030-55777-5_17)

Abstract

W-algebras are certain algebraic structures associated to a finite-dimensional Lie algebra Open image in new window and a nilpotent element f via Hamiltonian reduction. In this note we give a review of a recent approach to the study of (classical affine and quantum finite) W-algebras based on the notion of Lax type operators. For a finite-dimensional representation of Open image in new window a Lax type operator for W-algebras is constructed using the theory of generalized quasideterminants. This operator carries several pieces of information about the structure and properties of the W-algebras and shows the deep connection of the theory of W-algebras with Yangians and integrable Hamiltonian hierarchies of Lax type equations.

• Item Type: Book Sections
• Status: Published
• Glasgow Author(s) Enlighten ID: Valeri, Dr Daniele
• Authors: Valeri, D.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Publisher: Springer
• ISBN: 9783030557768
• Published Online: 08 August 2020
• Copyright Holders: Copyright © 2021 Springer Nature Switzerland AG
• First Published: First published in Quantum Theory and Symmetries: Proceedings of the 11th International Symposium, Montreal, Canada: 181-198
• Publisher Policy: Reproduced in accordance with the publisher copyright policy