Double affine Lie theory

代数是数学的一个分支，研究集合上的附加结构，类似于数字的加法和乘法。这样的结构化集合也被称为“代数”。李代数略有不同，类似于矩阵空间（数字数组）。我感兴趣的那些被称为“双仿射”：它们是矩阵，它们的元素是两个变量的多项式。仿射代数和李代数在数学物理中起着核心作用，在过去十年中，双仿射代数对这一理论科学分支的重要性一直在增加：因此，我的一些工作可能会引起物理学家的兴趣。

Algebra is a branch of mathematics which studies additional structures on sets which are similar to addition and multiplication of numbers. Such structured sets are also called by the generic name of "algebras". Lie algebras are slightly different and resemble spaces of matrices (arrays of numbers). Those that I am interested in are called "double affine": they are matrices with entries which are polynomials in two variables. Affine algebras and Lie algebras play a central role in mathematical physics and the importance of those of double affine type for this branch of theoretical science has been increasing over the last ten years: thus, some of my work may be of interest to physicists.