Permutation Group Algebras

Algebraic Combinatorics in Mathematical Chemistry. Methods and Algorithms. I. Permutation Groups and Coherent (cellular) Algebras

Let (G;) be a permutation group of degree n. Let V (G;) be the set of all square matrices of order n which commute with all permutation matrices corresponding to permutations from (G;): V (G;) is a matrix algebra which is called the centralizer algebra of (G;): In this paper we introduce the combinatorial analogue of centralizer algebras, namely coherent (cellular) algebras and consider the pro...

Indecomposable Representations and the Loop-space Operation1

For a certain class of algebras, including group-algebras of finite groups, we shall introduce a permutation in the set of isomorphismclasses of nonprojective indecomposable modules. This permutation is in essence given by the loop-space functor [2]. It is to be hoped that the study of this permutation may give some insight into the difficult problem of classifying indecomposable representation...

Primitivity of Permutation Groups, Coherent Algebras and Matrices

A coherent algebra is F-primitive if each of its non-identity basis matrices is primitive in the sense of Frobenius. We investigate the relationship between the primitivity of a permutation group, the primitivity of its centralizer algebra, and F-primitivity. The results obtained are applied to give new proofs of primitivity criteria for the exponentiations of permutation groups and of coherent...

Permutation Groups, a Related Algebra and a Conjecture of Cameron

We consider the permutation group algebra defined by Cameron and show that if the permutation group has no finite orbits, then no homogeneous element of degree one is a zero-divisor of the algebra. We proceed to make a conjecture which would show that the algebra is an integral domain if, in addition, the group is oligomorphic. We go on to show that this conjecture is true in certain special ca...

Permutation Group Algebras and Parking Functions