Asymptotic behaviour of Functional Identities

Gordienko, A. S.. "Asymptotic behaviour of Functional Identities." Serdica Mathematical Journal 38.1-3 (2012): 259-272. <http://eudml.org/doc/288278>.

@article{Gordienko2012,
abstract = {2010 Mathematics Subject Classification: Primary 16R60, Secondary 16R10, 15A03, 15A69.We calculate the asymptotics of functional codimensions fcn(A) and generalized functional codimensions gfc n (A) of an arbitrary not necessarily associative algebra A over a field F of any characteristic. Namely, fcn(A) ∼ gfcn(A) ∼ dim(A^2) · (dim A^n) as n → ∞ for any finite-dimensional algebra A. In particular, codimensions of functional and generalized functional identities satisfy the analogs of Amitsur’s and Regev’s conjectures. Also we precisely evaluate fcn(UT2(F)) = gfcn(UT2(F)) = 3^(n+1) − 2^(n+1).* Supported by post doctoral fellowship from Atlantic Association for Research in Mathematical Sciences (AARMS), Atlantic Algebra Centre (AAC), Memorial University of Newfoundland (MUN), and Natural Sciences and Engineering Research Council of Canada (NSERC).},
author = {Gordienko, A. S.},
journal = {Serdica Mathematical Journal},
keywords = {Functional Identity; Generalized Functional Identity; Codimension; Growth; Algebra; Amitsur’s Conjecture; Regev’s Conjecture},
language = {eng},
number = {1-3},
pages = {259-272},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Asymptotic behaviour of Functional Identities},
url = {http://eudml.org/doc/288278},
volume = {38},
year = {2012},
}

TY - JOUR
AU - Gordienko, A. S.
TI - Asymptotic behaviour of Functional Identities
JO - Serdica Mathematical Journal
PY - 2012
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 38
IS - 1-3
SP - 259
EP - 272
AB - 2010 Mathematics Subject Classification: Primary 16R60, Secondary 16R10, 15A03, 15A69.We calculate the asymptotics of functional codimensions fcn(A) and generalized functional codimensions gfc n (A) of an arbitrary not necessarily associative algebra A over a field F of any characteristic. Namely, fcn(A) ∼ gfcn(A) ∼ dim(A^2) · (dim A^n) as n → ∞ for any finite-dimensional algebra A. In particular, codimensions of functional and generalized functional identities satisfy the analogs of Amitsur’s and Regev’s conjectures. Also we precisely evaluate fcn(UT2(F)) = gfcn(UT2(F)) = 3^(n+1) − 2^(n+1).* Supported by post doctoral fellowship from Atlantic Association for Research in Mathematical Sciences (AARMS), Atlantic Algebra Centre (AAC), Memorial University of Newfoundland (MUN), and Natural Sciences and Engineering Research Council of Canada (NSERC).
LA - eng
KW - Functional Identity; Generalized Functional Identity; Codimension; Growth; Algebra; Amitsur’s Conjecture; Regev’s Conjecture
UR - http://eudml.org/doc/288278
ER -