The group of automorphisms of semigroup of endomorphisms of free commutative and free associative algebras

Varieties Characterized by their Endomorphisms

We show that two varieties X and Y with isomorphic endomorphism semigroups are isomorphic up to field automorphism if one of them is affine and contains a copy of the affine line. A holomorphic version of this result is due to the first author.

Constructing Endomorphism Rings of Large Finite Global Dimension

In this paper we study endomorphism rings of finite global dimension over a ring associated to a numerical semigroup. We construct these endomorphism rings in two ways, called the lazy and greedy construction. The first main result of this paper shows that the lazy construction enables us to obtain endomorphism rings of arbitrarily large global dimension. The second main result of this paper shows that the greedy construction gives us endomorphism rings which always have global dimension two. As a consequence, for a fixed numerical semigroup, the difference of the maximal possible value and th…

On automorphisms and endomorphisms of projective varieties

We first show that any connected algebraic group over a perfect field is the neutral component of the automorphism group scheme of some normal projective variety. Then we show that very few connected algebraic semigroups can be realized as endomorphisms of some projective variety X, by describing the structure of all connected subsemigroup schemes of End(X).

Chow Groups of Abelian Varieties and Beilinson's Conjecture

In the present paper we introduce the property AA of a subsemigroup of the endomorphism semigroup of an abelian variety, which holds for semigroup of endomorphisms of an abelian variety defined over a number field, and show that the orbit of any cycle under a semigroup with property AA in the Chow group $\otimes\Q$ has finite dimensional span.

曲面上的曲线与关联代数的模

Curves on surfaces and moduli of associative algebras

研究通过曲面上的曲线作为Fukaya范畴对象的A∞代数计算方法，展示如何利用Gauss字和可见多边形计算自交次数不超过三的浸入体的A∞积，并证明有限维代数可作为某些曲面的Lagrangian浸入的端射影代数。

Weight multiplicity free representations, $\frak g$-endomorphism algebras, and Dynkin polynomials

$\frak g$-endomorphism algebras form an interesting class of associative algebras related to the adjoint representation of a semisimple Lie algebra $\frak g$. These algebras were recently introduced by A.Kirillov, who used the term `family algebras'. Let $C_λ$ denote the $\frak g$-endomorphism algebra associated with a simple $\frak g$-module $V_λ$. Most of our results concern the case in which $C_λ$ is commutative, i.e., $V_λ$ is a weight multiplicity free $\frak g$-module. It is proved that $C_λ$ is a polynomial algebra if and only if $λ$ is minuscule. We also characterise in general the num…