题  目：Groebner-Shirshov Bases and Poincare-Birkhoff-Witt Theorem for Rota-Baxter Algebras

报告人：裴俊（兰州大学）

时  间：12月21日16：00-17：00

地  点：管研楼1518

摘  要：In the same way that an associative algebra gives a Lie algebra, a Rota-Baxter associative algebra also gives a Rota-Baxter Lie algebra, thus giving rise to a natural functor between the two corresponding categories. Then as in the case of associative algebras and Lie algebras, the adjoint functor defines the universal enveloping Rota-Baxter associative algebra of a Rota-Baxter Lie algebra. It is more difficult to prove a Poincare-Birkhoff-Witt (PBW) theorem for this enveloping algebra. For this purpose, we apply the method of Groebner-Shirshov bases. A consequence of the Rota-Baxter PBW theorem is that every Rota-Baxter Lie algebra can be embedded into a Rota-Baxter associative algebra.

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