Artículo
The structure of smooth algebras in Kapranov's framework for noncommutative geometry
Fecha de publicación:
11/2004
Editorial:
Academic Press Inc Elsevier Science
Revista:
Journal of Algebra
ISSN:
0021-8693
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
In Kapranov, M. Noncommutative geometry based on commutator expansions, J. reine angew. Math 505 (1998) 73-118, a theory of noncommutative algebraic varieties was proposed. Here we prove a structure theorem for the noncommutative coordinate rings of affine open subsets of such of those varieties which are smooth (Theorem 3.4). The theorem describes the local ring of a point as a truncation of a quantization of the enveloping Poisson algebra of a smooth commutative local algebra. An explicit descripition of this quantization is given in Theorem 2.5. A description of the A- module structure of the Poisson envelope of a smooth commutative algebra A was given in loc. cit., Theorem 4.1.3. However the proof given in loc. cit. has a gap. We fix this gap for A local (Theorem 1.4) and prove a weaker global result (Theorem 1.6).
Palabras clave:
COMMUTATOR FILTRATION
,
POISSON ALGEBRA
,
D-SMOOTH ALGEBRA
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Articulos(IMAS)
Articulos de INSTITUTO DE INVESTIGACIONES MATEMATICAS "LUIS A. SANTALO"
Articulos de INSTITUTO DE INVESTIGACIONES MATEMATICAS "LUIS A. SANTALO"
Citación
Cortiñas, Guillermo Horacio; The structure of smooth algebras in Kapranov's framework for noncommutative geometry; Academic Press Inc Elsevier Science; Journal of Algebra; 281; 2; 11-2004; 679-694
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