Let be a nite dimensional hereditary algebra over a nite eld k; H(() and C(() be respectively the Hall algebra and the composition algebra of ; P be the isomorphism classes of nite dimensional-modules and I the isomorphism classes of simple-modules. We deene and , 2 P, to be the right and left derivations of H(() respectively. By using these derivations and the action of the braid group on the ...

A semigroup S is said to have the compactness property, or CP for short, if each system of equations over a nite set of variables has an equivalent nite subsystem, that is, having exactly the same solutions in S. We prove that a completely 0-simple semigroup S satis es CP if and only if the group G in a Rees matrix representation S = M0(I; G; ;P) satis es this property. Further, a variety of co...

let g be a finite group and let $gk(g)$ be the prime graph of g. we assume that $n$ is an odd number. in this paper, we show that if $gk(g)=gk(b_n(p))$, where $ngeq 9$ and $pin {3,5,7}$, then g has a unique nonabelian composition factor isomorphic to $b_n(p)$ or $c_n(p)$ . as consequences of our result, $b_n(p)$ is quasirecognizable by its spectrum and also by a new proof, the validity of a con...

Using ltered Bowen-Franks group BF ? (A), we classify reducible shifts of nite type A with nite BF(A) up to ow equivalence. Using this result and some new development in C-algebras due to RRrdam and Cuntz, we classify non-simple Cuntz-Krieger algebras O A with nite K 0 (O A) up to stable isomorphism by the ltered K 0-group K ? 0 (O A); up to unital isomorphism by K ? 0 (O A) together with the d...

A theory of highest weight modules over an arbitrary nite-dimensional Lie su-peralgebra is constructed. A necessary and suucient condition for the nite-dimensionality of such modules is proved. Generic nite-dimensional irreducible representations are deened and an explicit character formula for such representations is written down. It is conjectured that this formula applies to any generic nite...

Compared to artificial metamaterials, where nano-fabrication complexities and finite-size inclusions can hamper the desired electromagnetic response, several natural materials like van der Waals crystals hold great promise for designing efficient nanophotonic devices in optical range. Here, we investigate unusual response of NiTe$_2$, a crystal type-II Dirac semimetal hosting Lorentz-violating ...

in this paper, we nd the relationships between module contractibility of abanach algebra and its ideals. we also prove that module contractibility ofa banach algebra is equivalent to module contractibility of its module uniti-zation. finally, we show that when a maximal group homomorphic image ofan inverse semigroup s with the set of idempotents e is nite, the moduleprojective tensor product ...

For a nite group G the commutativity degree denote by d(G) and dend:$$d(G) =frac{|{(x; y)|x, yin G,xy = yx}|}{|G|^2}.$$ In [2] authors found commutativity degree for some groups,in this paper we nd commutativity degree for a class of groups that have high nilpontencies.

0 Introduction We began in 4] a study of the Grothendieck group G(H) of the category of nite dimensional right comodules of a Hopf algebra H. We begin here the study of the representation theory of the algebras G(H) K obtained from G(H) by extending the scalars. Our primary motivation has been to try to establish Kaplansky's conjecture that if a nite dimensional cosemisimple Hopf algebra H over...