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Moscow Mathematical Journal, 2021, Volume 21, Number 2, Pages 383–399
DOI: https://doi.org/10.17323/1609-4514-2021-21-2-383-399
(Mi mmj797)
 

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
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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 $\mathrm{W}$-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.
Bibliographic databases:
Document Type: Article
MSC: 17B35, 16H99
Language: English
Citation: I. Losev, I. Panin, “Goldie ranks of primitive ideals and indexes of equivariant Azumaya algebras”, Mosc. Math. J., 21:2 (2021), 383–399
Citation in format AMSBIB
\Bibitem{LosPan21}
\by I.~Losev, I.~Panin
\paper Goldie ranks of primitive ideals and indexes of equivariant Azumaya algebras
\jour Mosc. Math.~J.
\yr 2021
\vol 21
\issue 2
\pages 383--399
\mathnet{http://mi.mathnet.ru/mmj797}
\crossref{https://doi.org/10.17323/1609-4514-2021-21-2-383-399}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85105320277}
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  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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