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Re-filtering and exactness of the Gelfand–Kirillov dimension

Authors
Journal
Bulletin des Sciences Mathématiques
0007-4497
Publisher
Elsevier
Publication Date
Volume
125
Issue
8
Identifiers
DOI: 10.1016/s0007-4497(01)01090-9
Keywords
  • Multi-Filtration
  • Gelfand–Kirillov Dimension
  • Exactness
  • Finitely Partitive Algebra
  • Semi-Commutative Algebra
Disciplines
  • Mathematics
  • Physics

Abstract

Abstract We prove that any multi-filtered algebra with semi-commutative associated graded algebra can be endowed with a locally finite filtration keeping up the semi-commutativity of the associated graded algebra. As consequences, we obtain that Gelfand–Kirillov dimension is exact for finitely generated modules and that the algebra is finitely partitive. Our methods apply to algebras of current interest like the quantized enveloping algebras, iterated differential operators algebras, quantum matrices or quantum Weyl algebras.

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