The centre of the modular affine vertex algebra

IF 1.5 1区 数学 Q1 MATHEMATICS Advances in Mathematics Pub Date : 2024-11-29 DOI:10.1016/j.aim.2024.110052
Tomoyuki Arakawa , Lewis Topley , Juan J. Villarreal
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Abstract

The Feigin–Frenkel theorem states that, over the complex numbers, the centre of the universal affine vertex algebra at the critical level is an infinite rank polynomial algebra. The first author and W. Wang observed that in positive characteristics, the universal affine vertex algebra contains a large central subalgebra known as the p-centre. They conjectured that at the critical level the centre should be generated by the Feigin–Frenkel centre and the p-centre. In this paper we prove the conjecture for classical simple Lie algebras for p larger than the Coxeter number, and for exceptional Lie algebras in large characteristics. Finally, we give an example which shows that at non-critical level the center is larger than the p-centre.
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Advances in Mathematics
Advances in Mathematics 数学-数学
CiteScore
2.80
自引率
5.90%
发文量
497
审稿时长
7.5 months
期刊介绍: Emphasizing contributions that represent significant advances in all areas of pure mathematics, Advances in Mathematics provides research mathematicians with an effective medium for communicating important recent developments in their areas of specialization to colleagues and to scientists in related disciplines.
期刊最新文献
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