Finitely Presented Algebras and Groups Defined by Permutation Relations *
نویسندگان
چکیده
The class of finitely presented algebras over a field K with a set of generators a1, . . . , an and defined by homogeneous relations of the form a1a2 · · · an = aσ(a)aσ(2) · · · aσ(n), where σ runs through a subset H of the symmetric group Sym n of degree n, is introduced. The emphasis is on the case of a cyclic subgroup H of Sym n of order n. A normal form of elements of the algebra is obtained. It is shown that the underlying monoid, defined by the same (monoid) presentation, has a group of fractions and this group is described. Properties of the algebra are derived. In particular, it follows that the algebra is a semiprimitive domain. Problems concerning the groups and algebras defined by arbitrary subgroups H of Sym n are proposed. keywords: symmetric presentation, finitely presented, semigroup algebra, monoid, group
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