Abstract:
Argument shift algebras in S(g)S(g) (where gg is a Lie algebra) are Poisson commutative subalgebras (with respect to the Lie-Poisson bracket), generated by iterated argument shifts of Poisson central elements. Inspired by the quantum partial derivatives on U(gld)U(gld) proposed by Gurevich, Pyatov, and Saponov, I and Georgy Sharygin showed that the quantum argument shift algebras are generated by iterated quantum argument shifts of central elements in U(gld)U(gld). In this talk, I will introduce a formula for calculating iterated quantum argument shifts and generators of the quantum argument shift algebras up to the second order, recalling the main theorem.
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Note the non-standard start time!