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Centers and Azumaya loci for finite W -algebras in positive characteristic.
- Source :
-
Mathematical Proceedings of the Cambridge Philosophical Society . Jul2022, Vol. 173 Issue 1, p35-66. 32p. - Publication Year :
- 2022
-
Abstract
- In this paper, we study the center Z of the finite W-algebra $${\mathcal{T}}({\mathfrak{g}},e)$$ associated with a semi-simple Lie algebra $$\mathfrak{g}$$ over an algebraically closed field $$\mathbb{k}$$ of characteristic p≫0, and an arbitrarily given nilpotent element $$e \in{\mathfrak{g}} $$ We obtain an analogue of Veldkamp's theorem on the center. For the maximal spectrum Specm(Z), we show that its Azumaya locus coincides with its smooth locus of smooth points. The former locus reflects irreducible representations of maximal dimension for $${\mathcal{T}}({\mathfrak{g}},e)$$. [ABSTRACT FROM AUTHOR]
- Subjects :
- *LIE algebras
*LOCUS (Mathematics)
*FINITE, The
Subjects
Details
- Language :
- English
- ISSN :
- 03050041
- Volume :
- 173
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Mathematical Proceedings of the Cambridge Philosophical Society
- Publication Type :
- Academic Journal
- Accession number :
- 157407905
- Full Text :
- https://doi.org/10.1017/S0305004121000414