On the unit group of Z-orders in finite dimensional algebras
Artem Lopatin | Omsk Branch of Institute of Mathematics - Russia
Technique for obtaining the algebraic PTT models, applications and analysis in two...
| Full text | |
| Author(s): |
Centrone, Lucio
Total Authors: 1
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| Document type: | Journal article |
| Source: | Journal of Pure and Applied Algebra; v. 223, n. 7, p. 2977-2996, JUL 2019. |
| Web of Science Citations: | 0 |
| Abstract | |
We prove a strict relation between the Gelfand-Kirillov (GK) dimension of the relatively free (graded) algebra of a PI-algebra and its (graded) exponent. As a consequence we show a Bahturin-Zaicev type result relating the GK dimension of the relatively free algebra of a graded PI-algebra and the one of its neutral part. We also get that the growth of the relatively free graded algebra of a matrix algebra is maximal when the grading is fine. Finally we compute the graded GK dimension of the matrix algebra with any grading and the graded GK dimension of any verbally prime algebra endowed with an elementary grading. (C) 2018 Elsevier B.V. All rights reserved. (AU) | |
| FAPESP's process: | 15/08961-5 - Growth of algebras with polynomial identities |
| Grantee: | Lucio Centrone |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 18/02108-7 - Identities in (non) associative algebras and related themes. |
| Grantee: | Lucio Centrone |
| Support Opportunities: | Regular Research Grants |