Learn More
Abstact We are discussing certain combinatorial and counting problems related to quadratic algebras. First we give examples which confirm the Anick conjecture on the minimal Hilbert series for algebras given by n generators and n(n−1) 2 relations for n 7. Then we investigate combinatorial structure of colored graph associated to relations of RIT algebra.(More)
We investigate relations between the properties of an algebra and its varieties of finite-dimensional module structures, on the example of the Jordan plane R = kx, y/(xy − yx − y 2). Complete description of irreducible components of the representation variety mod(R, n) obtained for any dimension n, it is shown that the variety is equidimen-sional. The(More)
We describe the complete set of pairwise non-isomorphic irreducible modules S α over the algebra R = kx, y/(xy − yx − y 2), and the rule how they could be glued to indecomposables. Namely, we show that Ext 1 k (S α , S β) = 0, if α = β. Also the set of all representations is described subject to the Jordan normal form of Y. We study then properties of the(More)
We consider the question of 'classificiation' of finite-dimensional modules over the Jordan algebra R = kx, 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(More)
  • 1