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This article is cited in 2 scientific papers (total in 2 papers)
The $p$-centre of Yangians and shifted Yangians
Jonathan Brundana, Lewis Topleyb a Department of Mathematics, University of Oregon, Eugene, OR 97403, USA
b School of Mathematics, Statistics and Actuarial Science,
University of Kent,
Canterbury,
CT2 7FS
United Kingdom
Abstract:
We study the Yangian $Y_n$ associated to the general linear Lie algebra $\mathfrak{gl}_n$ over a field of positive characteristic, as well as its shifted analog $Y_n(\sigma)$. Our main result gives a description of the centre of $Y_n(\sigma)$: it is a polynomial algebra generated by its Harish-Chandra centre (which lifts the centre in characteristic zero) together with a large $p$-centre. Moreover, $Y_n(\sigma)$ is free as a module over its center. In future work, it will be seen that every reduced enveloping algebra $U_\chi(\mathfrak{gl}_n)$ is Morita equivalent to a quotient of an appropriate choice of shifted Yangian, and so our results will have applications in classical representation theory.
Key words and phrases:
Modular Yangian, finite $W$-algebra, restricted Lie algebra, centre.
Citation:
Jonathan Brundan, Lewis Topley, “The $p$-centre of Yangians and shifted Yangians”, Mosc. Math. J., 18:4 (2018), 617–657
Linking options:
https://www.mathnet.ru/eng/mmj688 https://www.mathnet.ru/eng/mmj/v18/i4/p617
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Abstract page: | 163 | References: | 24 |
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