Algebras generated by two idempotents

An algebra generated by two sets of mutually orthogonal idempotents

For a field F and an integer d ≥ 1, we consider the universal associative F-algebra A generated by two sets of d+1 mutually orthogonal idempotents. We display four bases for the F-vector space A that we find attractive. We determine how these bases are related to each other. We describe how the multiplication in A looks with respect to our bases. Using our bases we obtain an infinite nested seq...

Idempotents in Group Algebras

In this survey we collect and present the classical and some recent methods to compute the primitive (central) idempotents in semisimple group algebras. MSC 2010. 20C05, 20C15, 16S34, 16U60.

Central Idempotents in Group Algebras

Vertex algebras generated by Lie algebras

In this paper we introduce a notion of vertex Lie algebra U , in a way a “half” of vertex algebra structure sufficient to construct the corresponding local Lie algebra L(U) and a vertex algebra V(U). We show that we may consider U as a subset U ⊂ V(U) which generates V(U) and that the vertex Lie algebra structure on U is induced by the vertex algebra structure on V(U). Moreover, for any vertex ...

The semigroup generated by the idempotents of a partition monoid

We study the idempotent-generated subsemigroup of the partition monoid. In the finite case this subsemigroup consists of the identity and all the singular partitions. In the infinite case, the subsemigroup is described in terms of certain parameters that measure how far a partition is from being a permutation. As one of several corollaries, we deduce Howie’s description from 1966 of the semigro...