Asymptotic behaviour of Functional Identities
Asymptotic behaviour of Functional Identities
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).
- Institute of Mathematics and Informatics Bulgaria
- Vrije Universiteit Brussel Belgium
- Bulgarian Academy of Sciences Bulgaria
Generalized Functional Identity, functional identity, growth, 512, Regev's conjecture, Growth, codimension, Amitsur’s Conjecture, Algebra, Functional Identity, Codimension, Regev’s Conjecture, Amitsur's conjecture, generalized functional identity
Generalized Functional Identity, functional identity, growth, 512, Regev's conjecture, Growth, codimension, Amitsur’s Conjecture, Algebra, Functional Identity, Codimension, Regev’s Conjecture, Amitsur's conjecture, generalized functional identity
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