This project is maintained by ysykimura
2019年7月12日(金) 17:30~18:30, 18:45~19:45
I-siteなんば 2F S1 (I-siteなんばへは，地下鉄御堂筋線大国町駅が最寄りです．)
Truncated point schemes of generic graded algebras
There have been several attempts to define the space associated to a noncommutative ring. For a graded algebra, one effective approach is to consider point modules. Artin-Tate-Van den Bergh showed that the point modules are parametrized by the point scheme, which is defined to be the inverse limit of the schemes called the truncated point schemes. When the algebra is commutative, the point scheme is exactly the associated projective scheme. Thus, for the noncommutative case, each point module may be considered as a “point” of the associated “noncommutative projective scheme”. In the first talk, starting with the definition of a point module, I give a basic idea to compute the point scheme, and explain how to count the components of the truncated point schemes for graded algebras with generic relations. This is a joint work with Alex Chirvasitu.
Feigin-Odesskii’s elliptic algebras
Feigin and Odesskii introduced a family of graded algebras, each of which is parametrized by an elliptic curve and some other data, and claimed a number of remarkable results in their series of papers. The family contains all higher dimensional Sklyanin algebras, which have been widely studied and recognized as important examples of regular algebras in the sense of Artin and Schelter. In ongoing joint work with Alex Chirvasitu and S. Paul Smith, we study the entire family of the algebras of Feigin and Odesskii from various perspectives. In the second talk, I will explain some properties of those algebras, including the nature of the point schemes and nice algebraic properties that have been obtained by using the quantum Yang-Baxter equation.