Commutant, construction of polynomial algebras and their applications
서의린
27동 325호
0
3193
02.24 08:46
| 구분 | 초청강연 |
|---|---|
| 일정 | 2026-03-30(월) 12:30~14:00 |
| 세미나실 | 27동 325호 |
| 강연자 | Ian Marquette (La Trobe University) |
| 담당교수 | 서의린 |
| 기타 |
I will review recent works were the notion of commutant of Poisson and Lie algebras were applied in different contexts of mathematical physics such as superintegrability and subalgebra chains. I will start with discussing the case of Cartan subalgebras [1,2] which allowed to present notion of algebraic Hamiltonian, integrals and symmetry algebra. This allowed to obtain polynomial algebras generalising the Racah algebra. I will point out how those approaches are providing insight in other context [3,4,5,6] and in particular subalgebras chains g ⊃ g′. I will discuss the case of Elliott su(3) ⊃ so(3) and seniority so(5) ⊃ su(2) × u(1) chains [4].
1.R Campoamor-Stursberg, D Latini, I Marquette, YZ Zhang, Algebraic (super-) integrability from commutants of subalgebras in universal enveloping algebras Journal of Physics A: Mathematical and Theoretical 56 (4), 045202 (2023)
2. R Campoamor-Stursberg ,D Latini, I Marquette, YZ Zhang, Polynomial algebras from commutants: Classical and quantum aspects of A_3, Journal of Physics A: Conf. Series 2667 012037 (2023)
3.R Campoamor-Stursberg, Ian Marquette, Decomposition of enveloping algebras of simple Lie algebras and their related polynomial algebras, Journal of Lie Theory 34 1 017-040 (2024)
4.R Campoamor-Stursberg ,D Latini, I Marquette, YZ Zhang, Polynomial algebras from Lie algebras reduction chains g ⸧g’ , Annals of Physics 459 169496 1-19 (2023)
5.R Campoamor-Stursberg ,D Latini, I Marquette, J Zhang, YZ Zhang, On the construction of polynomial Poisson algebras: a novel grading approach, Eur. Phys. J. Plus 141, 155 (2026)
6.R Campoamor-Stursberg ,D Latini, I Marquette, J Zhang, YZ Zhang, Polynomial algebra from Lie algebra reduction chain su(4) ⸧ su(2) x su(2): The supermultiplet model, Annals of Physics 485 170322 (2026)
