A note on locally finite group algebras

A Note on Locally Inverse Semigroup Algebras

Let R be a commutative ring and S a finite locally inverse semigroup. It is proved that the semigroup algebra R S is isomorphic to the direct product of Munn algebras M R GJ , mJ , nJ ;PJ with J ∈ S/J, where mJ is the number of R-classes in J , nJ the number of L-classes in J , and GJ a maximum subgroup of J . As applications, we obtain the sufficient and necessary conditions for the semigroup ...

a note on the power graph of a finite group

suppose $gamma$ is a graph with $v(gamma) = { 1,2, cdots, p}$and $ mathcal{f} = {gamma_1,cdots, gamma_p} $ is a family ofgraphs such that $n_j = |v(gamma_j)|$, $1 leq j leq p$. define$lambda = gamma[gamma_1,cdots, gamma_p]$ to be a graph withvertex set $ v(lambda)=bigcup_{j=1}^pv(gamma_j)$ and edge set$e(lambda)=big(bigcup_{j=1}^pe(gamma_j)big)cupbig(bigcup_{ijine(gamma)}{uv;uin v(gamma_i),vin ...

Algebras with Locally Finite Decomposition

We introduce the notion of locally finite decomposition rank, a structural property shared by many stably finite nuclear C∗-algebras. The concept is particularly relevant for Elliott’s program to classify nuclear C∗algebras by K-theory data. We study some of its properties and show that a simple unital C∗-algebra, which has locally finite decomposition rank, real rank zero and which absorbs the...

A Note on Semi-groups in a Locally Compact Group

Note on Lie algebras , finite groups and finite geometries

The subject of this note began with Thompson [Thl,2]. In the course of constructing his simple group Th, he considered the Lie algebra Lover iC of type Es. He constructed a decomposition L H1 ..L ... ..L H31 using a family H. {H1, ... , H31 } of Cartan algebras that are pairwise perpendicular with respect to the Killing form (he called this a "Dempwolff decomposition" of L; the construction was...