Multilinear approach to quantum Lie theory

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.