¹Universidad Nacional de Colombia, Bogotá, Colombia. Email: mareyesv@unal.edu.co

Gelfand-Kirillov dimension of Poincaré-Birkhoff-Witt (PBW for short) extensions was established by Matczuk ([15], Theorem A). Since PBW extensions are a particular example of skew PBW extensions (also called σ-PBW extensions), the aim of this paper is to compute this dimension for these extensions and hence generalize Matczuk's results for several algebras which can not be classified as PBW extensions.

Key words: Non-commutative algebras, Filtered and graded rings, PBW extensions, Skew quantum polynomials, Gelfand Kirillov dimension.

La dimensión de Gelfand-Kirillov de las extensiones de Poincaré-Birkhoff-Witt (abreviadas PBW) fue establecida por Matczuk ([15] Theorem A). Dado que las extensiones PBW son un ejemplo particular de las extensiones PBW torcidas (también llamadas extensiones σ-PBW), el objetivo de este artículo es calcular esta dimensión para dichas extensiones y así generalizar los resultados de Matczuk para varias álgebras que no pueden ser clasificadas como extensiones PBW.

Palabras clave: Álgebras no conmutativas, anillos filtrado graduados, extensiones PBW, polinomios cuánticos torcidos, dimensión de Gelfand-Kirillov.

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