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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Blomer, Valentin / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Echterhoff, Siegfried / Frahm, Jan / Gordina, Maria / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

IMPACT FACTOR 2018: 0.867

CiteScore 2018: 0.71

SCImago Journal Rank (SJR) 2018: 0.898
Source Normalized Impact per Paper (SNIP) 2018: 0.964

Mathematical Citation Quotient (MCQ) 2018: 0.71

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Volume 27, Issue 3


The variety of nilpotent elements and invariant polynomial functions on the special algebra Sn

Junyan Wei / Hao Chang / Xin Lu
Published Online: 2013-05-15 | DOI: https://doi.org/10.1515/forum-2012-0163


In the study of the variety of nilpotent elements in a Lie algebra, Premet conjectured that this variety is irreducible for any finite dimensional restricted Lie algebra. In this paper, with the assumption that the ground field is algebraically closed of characteristic p > 3, we confirm this conjecture for the Lie algebras of Cartan type S˜n and Sn. Moreover, we show that the variety of nilpotent elements in Sn is a complete intersection. Motivated by the proof of the irreducibility, we describe explicitly the ring of invariant polynomial functions on Sn.

Keywords: Variety of nilpotent elements; restricted Lie algebra; automorphism group; nilpotent orbits; invariant polynomial; complete intersection

MSC: 17B08; 17B50; 16W22; 17B40

About the article

Received: 2012-11-10

Revised: 2013-03-17

Published Online: 2013-05-15

Published in Print: 2015-05-01

Funding Source: Fund of ECNU for Overseas Studies

Funding Source: NSF of China

Award identifier / Grant number: 11126062

Funding Source: NSF of China

Award identifier / Grant number: 11201293

Funding Source: NSF of China

Award identifier / Grant number: 11271130

Funding Source: Innovation Program of Shanghai Municipal Education Commission

Award identifier / Grant number: 12ZZ038

Funding Source: ECNU Reward for Excellent Doctors in Academics

Citation Information: Forum Mathematicum, Volume 27, Issue 3, Pages 1689–1715, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2012-0163.

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