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Re-filtering and exactness of the Gelfand–Kirillov dimension

✍ Scribed by J.L. Bueso; J. Gómez-Torrecillas; F.J. Lobillo

Publisher
Elsevier Science
Year
2001
Tongue
French
Weight
176 KB
Volume
125
Category
Article
ISSN
0007-4497

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✦ Synopsis

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.  2001 Éditions scientifiques et médicales Elsevier SAS

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∗-Orderings and ∗-valuations on algebras
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✍ Murray Marshall 📂 Article 📅 2003 🏛 Elsevier Science 🌐 English ⚖ 198 KB

The paper considers the real \* -spectrum of a ÿnitely generated algebra with involution over C of ÿnite Gelfand-Kirillov dimension. It is shown that for such an algebra the stability indices associated to the real \* -spectrum are bounded by the Gelfand-Kirillov dimension, as in the commutative cas