Algebras and groups defined by permutation relations of alternating type

作者：Cedo Ferran; Jespers Eric; Okninski Jan^*

来源：Journal of Algebra, 2010, 324(6): 1290-1313.

DOI：10.1016/j.jalgebra.2010.07.014

• Semigroup ring
• Finitely presented
• Semigroup
• Jacobson radical
• Semiprimitive

The class of finitely presented algebras over a field K with a set of generators a(1),...,a(n) and defined by homogeneous relations of the form a(1)a(2)...a(n) = a(sigma(1))a(sigma(2))...a(sigma(n)), where sigma runs through Alt(n), the alternating group of degree n, is considered. The associated group, defined by the same (group) presentation, is described. A description of the Jacobson radical of the algebra is found. It turns out that the radical is a finitely generated ideal that is nilpotent and it is determined by a congruence on the underlying monoid, defined by the same presentation.

• 出版日期2010-9-15