We show a method to effectively compute the Wedderburn decomposition and the primitive central idempotents of a semisimple finite group algebra of an abelian-by-supersolvable group G from certain pairs of subgroups of G. In this paper F = Fq denotes a finite field with q elements and G is a finite group of order n such that FG is semisimple, or equivalently (q, n) = 1. The group algebra FG is a...

We use the technique of interactive theorem proving to develop the theory and an enumeration technique for finite idempotent relations. Starting from a short mathematical characterization of finite idempotents defined and proved in Isabelle/HOL, we derive first an iterative procedure to generate all instances of idempotents over a finite set. From there, we develop a more precise theoretical ch...

We prove that every semigroup S in which the idempotents form a sub-semigroup has an E-unitary cover with the same property. Furthermore, if S is E-dense or orthodox, then its cover can be chosen with the same property. Then we describe the structure of E-unitary dense semigroups. Our results generalize Fountain's results on semigroups in which the idempotents commute, and are analogous to thos...

We study a family of complex representations of the group GL n (o), where o is the ring of integers of a non-archimedean local field F. These representations occur in the restriction of the Grassmann representation of GL n (F) to its maximal compact subgroup GL n (o). We compute explicitly the transition matrix between a geometric basis of the Hecke algebra associated with the representation an...

The concept of strong spined product of semigroups is introduced. We first show that a semigroup S is a rpp-semigroup with left central idempotents if and only if S is a strong semilattice of left cancellative right stripes. Then, we show that such kind of semigroups can be described by the strong spined product of a C-rpp-semigroup and a right normal band. In particular, we show that a semigro...

A sum of exponentials of the form f(x) = exp (2 iN1x)+exp (2 iN2x)+ +exp (2 iNmx), where the Nk are distinct integers is called an idempotent trigonometric polynomial or, simply, an idempotent. It is known that for every p > 1; and every set S of the torus T = R=Z with jSj > 0; there are idempotents concentrated on S in the Lp sense. We sketch how this concentration phenomenon originated as a r...

A self-map f on the CW complex Z is a periodic homotopy idempotent if for some r 0 and p > 0 the iterates fr and fr+p are homotopic. Geoghegan and Nicas defined the rotation index RI(f) of such a map. They proved that for r = p = 1, the homotopy idempotent f splits if and only if RI(f) = 1, while for r = 0, the index RI(f) divides p2. We extend this to arbitrary p and r, and generalize various ...

Eilenberg has shown that there is a one-to-one correspondence between varieties of finite monoids and varieties of recognizable languages. In this paper, we give a description of a variety of languages close to the class of piecewise testable languages considered by I. Simon. The corresponding variety of monoids is the variety of J -trivial monoids with commuting idempotents. This result is the...

We generalize the word problem for groups, the formal language of all words in the generators that represent the identity, to inverse monoids. In particular, we introduce the idempotent problem, the formal language of all words representing idempotents, and investigate how the properties of an inverse monoid aer related to the formal language properties of its idempotent problem. In particular,...