A COMPENDIUM OF LIE STRUCTURES ON TENSOR PRODUCTS

摘要

It is demonstrated how a simple linear-algebraic technique used earlier to compute the low-degree cohomology of current Lie algebras, can be utilized to compute other kinds of structures on such Lie algebras, and discuss further generalizations, applications, and related questions. While doing so, seemingly diverse topics are touched upon such as associative algebras of infinite representation type, Horn-Lie structures, Poisson brackets of hydrodynamic type, Novikov algebras, simple Lie algebras in small characteristics, and Koszul dual operads. Bibliography: 40 titles.