Total Ring of fractions of skew PBW extensions (2014)
We study the Gelfand Kirillov conjecture for some algebras and rings, we use similar tools for studying the ring of fractions of skew PBW extensions, establishing isomorphisms between algebras and rings. Particular cases are studied as is the case of Lie algebras and Abstract. Weyl algebras to which we devote the entire first chapter of preliminaries, then we make a collection about the conjecture for the classical and quantum case in the second chapter. To finally conclude with skew PBW extensions, which cover many algebras under study.