6533b857fe1ef96bd12b4638

RESEARCH PRODUCT

Multialternating Jordan polynomials and codimension growth of matrix algebras

Mikhail ZaicevAntonio Giambruno

subject

Numerical AnalysisJordan matrixPolynomialPure mathematicsAlgebra and Number TheoryJordan algebraMathematics::Rings and AlgebrasJordan algebraZero (complex analysis)Polynomial identityExponential growthNoncommutative geometryCodimensionsMatrix polynomialsymbols.namesakeMatrix (mathematics)symbolsDiscrete Mathematics and CombinatoricsGeometry and TopologyMathematicsCharacteristic polynomial

description

Abstract Let R be the Jordan algebra of k  ×  k matrices over a field of characteristic zero. We exhibit a noncommutative Jordan polynomial f multialternating on disjoint sets of variables of order k 2 and we prove that f is not a polynomial identity of R . We then study the growth of the polynomial identities of the Jordan algebra R through an analysis of its sequence of Jordan codimensions. By exploiting the basic properties of the polynomial f , we are able to prove that the exponential rate of growth of the sequence of Jordan codimensions of R in precisely k 2 .

yearjournalcountryeditionlanguage
2007-04-01
http://hdl.handle.net/10447/32507