Multilinear Quantum Lie Operators

Plática dada por Vladislav Kharchenko (FES Cuautitlán, UNAM) en el marco del evento Graded Algebras, Geometry and related Topics para celebrar el 60 aniversario de Adolfo Sánchez Valenzuela el martes 15 de noviembre del 2016 en la Universidad Autónoma de Yucatán (UADY)

Abstract:
The numerous attempts over the previous 15-20 years to define a quantum Lie algebra as an elegant algebraic object with a binary "quantum" Lie bracket have not been widely accepted. In the talk we discuss an alternative approach that includes multivariable operations.

There are many fields in which multivariable operations replace the Lie bracket, such as investigations of skew derivations in ring theory, local analytic loop theory, and theoretical research on generalizations of Nambu mechanics.

Among the problems discussed in the talk are the following: multilinear quantum Lie operations, the principle generic quantum Lie operation, the basis of symmetric generic operations, Shestakov-Umirbaev operations for the Lie theory of nonassociative products. We also discuss extent to which a natural binary bracket may define somerthing that looks like a "quantum Lie algebra" inside of quantizations of Kac--Moody type in line with the PBW theorem for character Hopf algebras.

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