Geodesic
A compendium of Lie structures on tensor products
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 25, Tome 414 (2013), pp. 40-81

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We demonstrate how a simple linear-algebraic technique used earlier to compute 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, we touch upon such seemingly diverse topics as associative algebras of infinite representation type, Hom-Lie structures, Poisson brackets of hydrodynamic type, Novikov algebras, simple Lie algebras in small characteristics, and Koszul dual operads. 
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     author = {P. Zusmanovich},
     title = {A compendium of {Lie} structures on tensor products},
     journal = {Zapiski Nauchnykh Seminarov POMI},
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     volume = {414},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2013_414_a3/}
}
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P. Zusmanovich. A compendium of Lie structures on tensor products. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 25, Tome 414 (2013), pp. 40-81. http://geodesic.mathdoc.fr/item/ZNSL_2013_414_a3/