Geodesic
Quantized symplectic actions and 𝑊-algebras
Losev, Ivan1
1 Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139
Journal of the American Mathematical Society, Tome 23 (2010) no. 1, pp. 35-59

Voir la notice de l'article provenant de la source American Mathematical Society

With a nilpotent element in a semisimple Lie algebra $\mathfrak {g}$ one associates a finitely generated associative algebra $\mathcal {W}$ called a $W$-algebra of finite type. This algebra is obtained from the universal enveloping algebra $U(\mathfrak {g})$ by a certain Hamiltonian reduction. We observe that $\mathcal {W}$ is the invariant algebra for an action of a reductive group $G$ with Lie algebra $\mathfrak {g}$ on a quantized symplectic affine variety and use this observation to study $\mathcal {W}$. Our results include an alternative definition of $\mathcal {W}$, a relation between the sets of prime ideals of $\mathcal {W}$ and of the corresponding universal enveloping algebra, the existence of a one-dimensional representation of $\mathcal {W}$ in the case of classical $\mathfrak {g}$ and the separation of elements of $\mathcal {W}$ by finite-dimensional representations.
DOI : 10.1090/S0894-0347-09-00648-1

Losev, Ivan 1

1 Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139 
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Losev, Ivan. Quantized symplectic actions and 𝑊-algebras. Journal of the American Mathematical Society, Tome 23 (2010) no. 1, pp. 35-59. doi: 10.1090/S0894-0347-09-00648-1

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