# Moscow Mathematical Journal

Volume 18, Issue 4, October–December 2018 pp. 617–657.

The *p*-Centre of Yangians and Shifted Yangians

**Authors**:
Jonathan Brundan (1) and Lewis Topley (2)

**Author institution:**(1) Department of Mathematics, University of Oregon, Eugene, OR 97403, USA

(2) School of Mathematics, Statistics and Actuarial Science,
University of Kent,
Canterbury,
CT2 7FS
United Kingdom

**Summary: **

We study the Yangian *Y _{n}* associated to the general linear
Lie algebra 𝔤𝔩

_{n}over a field of positive characteristic, as well as its shifted analog

*Y*(σ). Our main result gives a description of the centre of

_{n}*Y*(σ): it is a polynomial algebra generated by its

_{n}*Harish-Chandra centre*(which lifts the centre in characteristic zero) together with a large

*p*-centre. Moreover,

*Y*(σ) is free as a module over its center. In future work, it will be seen that every reduced enveloping algebra

_{n}*U*

_{χ}(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.

2010 Math. Subj. Class. Primary: 17B37.

**Keywords:**Modular Yangian, finite

*W*-algebra, restricted Lie algebra, centre.

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