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.
Giambruno A., la Mattina D., Milies C.P. (2021). Understanding star-fundamental algebras. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 149(8), 3221-3233 [10.1090/proc/15458].
Understanding star-fundamental algebras
la Mattina D.
;
2021-01-01
Abstract
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.
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