Rota–Baxter algebra
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In mathematics, a Rota–Baxter algebra is an associative algebra, together with a particular linear map which satisfies the Rota–Baxter identity. It appeared first in the work of the American mathematician Glen E. Baxter[1] in the realm of probability theory. Baxter's work was further explored from different angles by Gian-Carlo Rota,[2][3][4] Pierre Cartier,[5] and Frederic V. Atkinson,[6] among others. Baxter’s derivation of this identity that later bore his name emanated from some of the fundamental results of the famous probabilist Frank Spitzer in random walk theory.[7][8]
In the 1980s, the Rota-Baxter operator of weight 0 in the context of Lie algebras was rediscovered as the operator form of the classical Yang–Baxter equation,[9] named after the well-known physicists Chen-Ning Yang and Rodney Baxter.
The study of Rota–Baxter algebras experienced a renaissance this century, beginning with several developments, in the algebraic approach to renormalization of perturbative quantum field theory,[10] dendriform algebras, associative analogue of the classical Yang–Baxter equation[11] and mixable shuffle product constructions.[12]