Algebra seminar - Tuan Pham
| Dates: | 18 March 2025 |
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| Times: | 14:00 - 15:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Who is it for: | University staff, External researchers, Current University students |
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| Speaker: | Tuan Pham |
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Title: The orbit method for the Virasoro algebra
Abstract: Let W = Ct^{-1}\del_t be the Witt algebra of algebraic vector fields on C* and let Vir be the Virasoro algebra, the unique nontrivial central extension of W. In Sierra 2022, it was shown that Poisson primitive ideals of S(W) and S(Vir) can be constructed from elements of W* and Vir* of a particular form, called local functions. In this talk, we show how to use a local function on W or Vir to construct a representation of the Lie algebra. We further show that the annihilators of these representations are new completely prime primitive ideals of U(W) and U(Vir). We use this to define a Dixmier map from the Poisson primitive spectrum of S(Vir), respectively S(W), to the primitive spectrum of U(Vir), respectively U(W), successfully extending the orbit method from finite-dimensional solvable Lie algebras to the countable-dimensional setting.
Our method involves new ring homomorphisms from U(W) to the tensor product of a localized Weyl algebra and the enveloping algebra of a finite-dimensional solvable subquotient of W. We further show that the kernels of these homomorphisms are intersections of the primitive ideals constructed from natural subsets of W*.
Speaker
Tuan Pham
Organisation: University of Edinburgh
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Frank Adams 1
Alan Turing Building
Manchester
