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BASES FOR QUANTUM ALGEBRAS AND SKEW POINCARÉ-BIRKHOFF-WITT EXTENSIONS
BASES PARA ÁLGEBRAS CUÁNTICAS Y EXTENSIONES TORCIDAS DE POINCARÉ-BIRKHOFF-WITT
Keywords:
Quantum algebras, skew Poincaré-Birkhoff-Witt (en)Álgebras cuánticas, extensiones torcidas de Poincaré-Birkhoff-Witt, lema del diamante. (es)
Considering quantum algebras and skew Poincaré-Birkhoff-Witt (PBW for short) extensions defined by a ring and a set of variables with relations between them, we are interesting in finding a criteria and some algorithms which allow us to decide whether an algebraic structure, defined by variables and relations between them, can be expressed as a skew PBW extension, so that the base of the structure is determined. Finally, we illustrate our treatment with examples concerning quantum physics.
Para las álgebras cuánticas y las extensiones torcidas de Poincaré-Birkhoff-Witt definidas por un anillo y un conjunto de variables con relaciones entre ellas, estamos interesados en establecer un criterio y algunos algoritmos que nos permitan decidir si una estructura algebraica, definida en términos de generadores y relaciones, puede expresarse como una extensión torcida de Poincaré-Birkhoff-Witt, de manera que se determine la base de la misma. Ilustramos nuestro tratamiento con diversas álgebras de la física cuántica.
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