Seminar talk, 20 November 2024, 16:00: Difference between revisions
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| abstract = Argument shift algebras in <math>S(g)</math> (where <math>g</math> 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 <math>U(gl_d)</math> 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 <math>U(gl_d)</math>. 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. | | abstract = Argument shift algebras in <math>S(g)</math> (where <math>g</math> 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 <math>U(gl_d)</math> 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 <math>U(gl_d)</math>. 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. | ||
Note the non-standard start time! | |||
| video = | ''Note the non-standard start time!'' | ||
| slides = | | video = https://video.gdeq.org/GDEq-zoom-seminar-20241120-Yasushi_Ikeda.mp4 | ||
| slides = [[Media:Shifts_in_gld.pdf|Shifts_in_gld.pdf]] | |||
| references = | | references = | ||
| 79YY-MM-DD = 7975-88-79 | | 79YY-MM-DD = 7975-88-79 | ||
}} | }} | ||
Latest revision as of 08:40, 4 January 2025
Speaker: Yasushi Ikeda
Title: Quantum argument shifts in general linear Lie algebras
Abstract:
Argument shift algebras in (where 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 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 . 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.
Note the non-standard start time!
Video
Slides: Shifts_in_gld.pdf