Double affine Lie theory

代数是数学的一个分支，它研究集合上的附加结构，类似于数的加法和乘法。这种结构化集合也被称为“代数”的总称。李代数略有不同，类似于矩阵空间（数组）。 那些我感兴趣的是所谓的“双仿射”：他们是矩阵的条目是多项式在两个变量。仿射代数和李代数发挥了核心作用，在数学物理和重要性的双仿射型为这分支的理论科学一直在增加在过去十年：因此，我的一些工作可能感兴趣的物理学家。

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.