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We study the cyclic homology for a class of noncommutative polynomial rings known as skew PBW extensions. We obtain explicit computations for some important families of such extensions over fields. In particular, we consider the cyclic homology of skew PBW extensions of derivation type, certain classes of Ore extensions, operator algebras, difusion algebras, quantum algebras and 3-dimensional skew polynomial algebras. Resumen Estudiamos la homologia ciclica de una clase de anillos de polinomios no conmutativos denominados extensiones PBW torcidas. Obtenemos calculos explicitos para algunas familias importantes de este tipo de extensiones sobre cuerpos. En particular, consideramos la homologia ciclica de las extensiones PBW torcidas de tipo derivacion, ciertas clases de extensiones de Ore, algebras de operadores, algebras de difusion, algebras cuanticas y algebras de polinomios torcidos 3-dimensionales.

Some Remarks About the Cyclic Homology of Skew PBW Extensions / Algunas observaciones sobre la homología cíclica de extensiones PBW torcidas