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arXiv · 1802.05651

Goldie ranks of primitive ideals and indexes of equivariant Azumaya algebras

Ivan Losev·Ivan Panin
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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 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.

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Ivan Losev, Ivan Panin. 2018-02-15. Goldie ranks of primitive ideals and indexes of equivariant Azumaya algebras. https://arxiv.org/abs/1802.05651

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