6533b828fe1ef96bd1287ae3
RESEARCH PRODUCT
Understanding star-fundamental algebras
D. La MattinaAntonio GiambrunoCésar Polcino Miliessubject
Computer Science::Machine LearningInvolutionPure mathematicsStar-fundamentalApplied MathematicsGeneral MathematicsStar (graph theory)Polynomial identityComputer Science::Digital LibrariesSettore MAT/02 - AlgebraStatistics::Machine LearningIDEAIS (ÁLGEBRA)Computer Science::Mathematical SoftwareComputer Science::Programming LanguagesInvolution (philosophy)Mathematicsdescription
Star-fundamental algebras are special finite dimensional algebras with involution ∗ * over an algebraically closed field of characteristic zero defined in terms of multialternating ∗ * -polynomials. We prove that the upper-block matrix algebras with involution introduced in Di Vincenzo and La Scala [J. Algebra 317 (2007), pp. 642–657] are star-fundamental. Moreover, any finite dimensional algebra with involution contains a subalgebra mapping homomorphically onto one of such algebras. We also give a characterization of star-fundamental algebras through the representation theory of the symmetric group.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2021-05-18 |