In mathematics, specifically representation theory, tilting theory describes a way to relate the module categories of two algebras using so-called tilting modules and associated tilting functors. Here, the second algebra is the endomorphism algebra of a tilting module over the first algebra. Tilting theory was motivated by the introduction of reflection functors by Joseph Bernšteĭn, Israel Gelfand, and V. A. Ponomarev; these functors were used to relate representations of two quivers. These functors were reformulated by Maurice Auslander, , and Idun Reiten, and generalized by Sheila Brenner and Michael C. R. Butler who introduced tilting functors. Dieter Happel and Claus Michael Ringel defined tilted algebras and tilting modules as further generalizations of this. (Wikipedia).
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