Seminar talk, 6 March 2024: Difference between revisions
Created page with "{{Talk | speaker = Georgy Sharygin | title = Deformation quantisation of the argument shift on <math>U\mathfrak{gl}(n)</math> | abstract = Argument shift algebras are the commutative subalgebras in the symmetric algebras of a Lie algebra, generated by the iterated derivations (in direction of a constant vector field) of Casimir elements in <math>S\mathfrak{gl}(n)</math>. In particular all these quasiderivations do mutually commute. In my talk I will show that a similar s..." |
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| title = Deformation quantisation of the argument shift on <math>U\mathfrak{gl}(n)</math> | | title = Deformation quantisation of the argument shift on <math>U\mathfrak{gl}(n)</math> | ||
| abstract = Argument shift algebras are the commutative subalgebras in the symmetric algebras of a Lie algebra, generated by the iterated derivations (in direction of a constant vector field) of Casimir elements in <math>S\mathfrak{gl}(n)</math>. In particular all these quasiderivations do mutually commute. In my talk I will show that a similar statement holds for the algebra <math>U\mathfrak{gl}(n)</math> and its quasiderivations: namely, I will show that iterated quasiderivations of the central elements of <math>U\mathfrak{gl}(n)</math> with respect to a constant quasiderivation do mutually commute. Our proof is based on the existence and properties of "Quantum Mischenko-Fomenko" algebras, and (which is worse) cannot be extended to other Lie algebras, but we believe that the fact that the "shift operator" can be raised to <math>U\mathfrak{gl}(n)</math> is an interesting fact. | | abstract = Argument shift algebras are the commutative subalgebras in the symmetric algebras of a Lie algebra, generated by the iterated derivations (in direction of a constant vector field) of Casimir elements in <math>S\mathfrak{gl}(n)</math>. In particular all these quasiderivations do mutually commute. In my talk I will show that a similar statement holds for the algebra <math>U\mathfrak{gl}(n)</math> and its quasiderivations: namely, I will show that iterated quasiderivations of the central elements of <math>U\mathfrak{gl}(n)</math> with respect to a constant quasiderivation do mutually commute. Our proof is based on the existence and properties of "Quantum Mischenko-Fomenko" algebras, and (which is worse) cannot be extended to other Lie algebras, but we believe that the fact that the "shift operator" can be raised to <math>U\mathfrak{gl}(n)</math> is an interesting fact. | ||
| video = | | video = https://video.gdeq.org/GDEq-zoom-seminar-20240306-Georgy_Sharygin.mp4 | ||
| slides = | | slides = | ||
| references = | | references = | ||
| 79YY-MM-DD = 7975-96-86 | | 79YY-MM-DD = 7975-96-86 | ||
}} | }} | ||
Latest revision as of 08:40, 4 January 2025
Speaker: Georgy Sharygin
Title: Deformation quantisation of the argument shift on
Abstract:
Argument shift algebras are the commutative subalgebras in the symmetric algebras of a Lie algebra, generated by the iterated derivations (in direction of a constant vector field) of Casimir elements in . In particular all these quasiderivations do mutually commute. In my talk I will show that a similar statement holds for the algebra and its quasiderivations: namely, I will show that iterated quasiderivations of the central elements of with respect to a constant quasiderivation do mutually commute. Our proof is based on the existence and properties of "Quantum Mischenko-Fomenko" algebras, and (which is worse) cannot be extended to other Lie algebras, but we believe that the fact that the "shift operator" can be raised to is an interesting fact.
Video