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- Peter J. Cameron, Natalia Iyudu
- J. Symb. Comput.
- 2007

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 6 7. Then we investigate combinatorial structure of colored graph associated to relations of RIT algebra.… (More)

We consider the class of crossed products of noetherian domains with universal enveloping algebras of Lie algebras. For algebras from this class we give a sufficient condition for the existence of projective non-free modules. This class includes Weyl algebras and universal envelopings of Lie algebras, for which this question, known as noncommutative Serre’s… (More)

- Natalia Iyudu, Stanislav Shkarin
- Combinatorica
- 2017

Throughout this article K is an arbitrary field, Z+ is the set of non-negative integers and N is the set of positive integers. For a set X, K〈X〉 stands for the free associative algebra over K generated by X. We deal with quadratic algebras, that is, algebras R given as K〈X〉/I, where I is the ideal in K〈X〉 generated by a collection of homogeneous elements… (More)

We give an effective solution of the conjugacy problem for two by two matrices over the polynomial ring in one variable over a finite field.

- Natalia K. Iyudu
- 2012

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 = k〈x, y〉/(xy − yx− y). Complete description of irreducible components of the representation variety mod(R,n) obtained for any dimension n, it is shown that the variety is equidimensional. The… (More)

- Natalia K. Iyudu
- 2009

We consider the question of ’classificiation’ of finite-dimensional modules over the Jordan algebra R = k〈x, y〉/(xy − yx− y). 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)

- Natalia K. Iyudu
- 2008

We describe the complete set of pairwise non-isomorphic irreducible modules Sα over the algebra R = k〈x, y〉/(xy − yx − y ), and the rule how they could be glued to indecomposables. Namely, we show that Ext1k(Sα, Sβ) = 0, if α 6= β. Also the set of all representations is described subject to the Jordan normal form of Y . We study then properties of the image… (More)

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