Non-commutative Laurent phenomenon for two variables
We prove the non-commutative Laurent phenomenon for two variables.
math.AG↗
arXiv subjects
Alexandr Usnich
Publications and source records attributed to Alexandr Usnich.
The action of the Cremona group on the non-commutative ring
The Cremona group acts on the field of two independent commutative variables over complex numbers. We provide a non-commutative ring that is an analog of non-commutative field of two independent variables and prove that the Cremona group embeds in the group of outer automorphisms of this ring. First proof of this result is technical, the second one is conceptual and gives a way to obtain non-commutative rings from the bounded derived categories of coherent sheaves.
math.AG↗
Symplectic automorphisms of CP^2 and the Thompson group T
We explain how to construct a morphism from the group of birational automorphisms of CP^2 preserving the logarithmic Poisson bracket to the Thompson group T. Than we give a linear representation of the former group, provide some information about Thompson group T and give it's new presentation in terms of generators and relations, and speculate about the presentation of the group of birational symplectomorphisms.
math.AG↗