Double affine Lie theory

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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.