Artem Lopatin | Omsk Branch of Institute of Mathematics - Russia
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| Full text | |
| Author(s): |
Lopatin, Artem A.
[1]
Total Authors: 1
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| Affiliation: | [1] SB RAS, Sobolev Inst Math, Omsk Branch, Fed State Budgetary Estab, Omsk 644099 - Russia
Total Affiliations: 1
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| Document type: | Journal article |
| Source: | Journal of Algebra; v. 371, p. 350-366, DEC 1 2012. |
| Web of Science Citations: | 4 |
| Abstract | |
Denote by C-n,C-d the nilpotency degree of a relatively free algebra generated by d elements and satisfying the identity x(n) = 0. Under assumption that the characteristic p of the base field is greater than n/2, it is shown that C-n,C-d < n(log2(3d+2)+1) and C-n,C-d < 4. 2(n/2)d. In particular, it is established that the nilpotency degree C-n,C-d has a polynomial growth in case the number of generators d is fixed and p > n/2. For p not equal 2 the nilpotency degree C-4,C-d is described with deviation 3 for all d. As an application, a finite generating set for the algebra R-GL(n) of GL(n)-invariants of d matrices is established in terms of C-n,C-d. Several conjectures are formulated. (C) 2012 Elsevier Inc. All rights reserved. (AU) | |
| FAPESP's process: | 11/51047-1 - Artem Lopatin | Omsk Branch of Institute of Mathematics - Russia |
| Grantee: | Ivan Chestakov |
| Support Opportunities: | Research Grants - Visiting Researcher Grant - International |