Irreducible components of the Jordan varieties

Details Irreducible components of the Jordan varieties Irreducible components of the Jordan varieties

2009-03-23

arxiv.org/abs/0903.3820v2

Mathematics

Representation Theory

35 pages

Scientific paper

We consider the question on 'classificiation' of finite-dimensional modules over the Jordan algebra $R=k< x,y>/ (xy-yx-y^2)$. Complete description of irreducible components of the representation variety $mod (R,n)$ of Jordan algebra is given for any dimension $n$. It is obtained on the basis of the stratification of this variety related to the Jordan normal form of $Y$. Any irreducible component of the representation variety contains only one stratum related to a certain partition of $n$ and is the closure of that stratum. The number of irreducible components therefore is equal to the number of partitions of $n$.

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