报告题目: The group of automorphisms of the algebra of one-sided inverses 

of a polynomial algebra

报告人:Professor Vladimir Bavula (Universiyt of Sheffield, UK)

报告时间:2018年5月18日14:00-15:00

报告地点:数学楼二楼学术报告厅

 

摘要: The algebra S(n) of one-sided inverses of the   polynomial 

algebra P(n) in n variables is obtained from the polynomial algebra 

P(n) by adding one-sided (but not two-sided) inverses of its canonical 

generators. The algebra S(n) is a non-commutative, non-Noetherian 

algebra which is not a domain. It is canonically isomorphic to the 

algebra of scalar integro-differential operators.

  It has properties that are mixture of properties of the polynomial 

algebra P(n) and the Weyl algebra A(n).

Properties of the algebra S(n) will be explained and a set of  explicit 

generators of its group of automorphisms will be given. The structure 

of the automorphism group of S(n) will be discussed.

 

 

报告题目: Localizable and weakly left localizable rings

报告人:Professor Vladimir Bavula (Universiyt of Sheffield, UK)

报告地点 2018年5月18日15:00-16:00

报告地点:数学楼二楼学术报告厅

摘要: Two new classes of rings are introduced - the class of left

localizable and the class of weakly left localizable rings. These are 

huge classes of rings.

Characterizations of them are given.

 

 

报告题目: Generalized Schur's Theorem

报告人:Professor Kaiming Zhao (Wilfrid Laurier University, Canada)

报告地点 2018年5月18日16:00-17:00

报告地点:数学楼二楼学术报告厅

摘要: More than 100 years ago, Schur proved that the maximal  dimension of   abelian subalgebras of the n by n matrix algebra  is $/frac{n^2}{4}+1$ if $n$ is even, and $(n+1)(n-1)/4+1$ if $n$ is odd. I will give a generalization of this theorem.