6533b823fe1ef96bd127e254
RESEARCH PRODUCT
Polynomial identities for the Jordan algebra of upper triangular matrices of order 2
Fabrizio MartinoPlamen Koshlukovsubject
Pure mathematicsPolynomialAlgebra and Number TheoryJordan algebraTriangular matrixJordan polynomial identities graded upper triangularCyclic groupField (mathematics)CodimensionBasis (universal algebra)CombinatoricsSettore MAT/02 - AlgebraOrder (group theory)Mathematicsdescription
Abstract The associative algebras U T n ( K ) of the upper triangular matrices of order n play an important role in PI theory. Recently it was suggested that the Jordan algebra U J 2 ( K ) obtained by U T 2 ( K ) has an extremal behaviour with respect to its codimension growth. In this paper we study the polynomial identities of U J 2 ( K ) . We describe a basis of the identities of U J 2 ( K ) when the field K is infinite and of characteristic different from 2 and from 3. Moreover we give a description of all possible gradings on U J 2 ( K ) by the cyclic group Z 2 of order 2, and in each of the three gradings we find bases of the corresponding graded identities. Note that in the graded case we need only an infinite field K , char K ≠ 2 .
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2012-11-01 |