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This article is cited in 3 scientific papers (total in 3 papers)
Goldie ranks of primitive ideals and indexes of equivariant Azumaya algebras
I. Loseva, I. Paninb a Department of Mathematics, Yale University, New Haven, CT, USA
b St. Petersburg branch of V.A. Steklov Mathematical Institute, St. Petersburg, Russian Federation
Abstract:
Let $\mathfrak{g}$ be a semisimple Lie algebra. We establish a new relation between the Goldie rank of a primitive ideal $\mathcal{J}\subset U(\mathfrak{g})$ and the dimension of the corresponding irreducible representation $V$ of an appropriate finite $\mathrm{W}$-algebra. Namely, we show that $\operatorname{Grk}(\mathcal{J}) \leqslant \dim V/d_V$, where $d_V$ is the index of a suitable equivariant Azumaya algebra on a homogeneous space. We also compute $d_V$ in representation theoretic terms.
Key words and phrases:
azumaya algebras, index, primitive ideals, Goldie ranks, W-algebras.
Citation:
I. Losev, I. Panin, “Goldie ranks of primitive ideals and indexes of equivariant Azumaya algebras”, Mosc. Math. J., 21:2 (2021), 383–399
Linking options:
https://www.mathnet.ru/eng/mmj797 https://www.mathnet.ru/eng/mmj/v21/i2/p383
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Abstract page: | 79 | References: | 18 |
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