6533b7d2fe1ef96bd125eba9
RESEARCH PRODUCT
Finite-dimensional non-associative algebras and codimension growth
Mikhail ZaicevAntonio GiambrunoIvan P. Shestakovsubject
Discrete mathematicsPure mathematicsJordan algebraApplied MathematicsJordan algebraNon-associative algebraSubalgebraUniversal enveloping algebraPolynomial identityExponential growthCodimensionsPolynomial identityCodimensionsExponential growthJordan algebraQuadratic algebraAlgebra representationDivision algebraCellular algebraPOLINÔMIOSMathematicsdescription
AbstractLet A be a (non-necessarily associative) finite-dimensional algebra over a field of characteristic zero. A quantitative estimate of the polynomial identities satisfied by A is achieved through the study of the asymptotics of the sequence of codimensions of A. It is well known that for such an algebra this sequence is exponentially bounded.Here we capture the exponential rate of growth of the sequence of codimensions for several classes of algebras including simple algebras with a special non-degenerate form, finite-dimensional Jordan or alternative algebras and many more. In all cases such rate of growth is integer and is explicitly related to the dimension of a subalgebra of A. One of the main tools of independent interest is the construction in the free non-associative algebra of multialternating polynomials satisfying special properties.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2011-07-01 | Advances in Applied Mathematics |