In this paper we introduce a new class of double coset Cayley digraphs induced by quasigroups. These graphs can be considered as the generalization of Double Coset Cayley Digraphs induced by loops. Moreover, various graph properties are expressed in terms of algebraic properties. This did not attract much attention in the literature.

Using sigma-model approach, we study a class of coset spaces with torsion which compactify the D = 26 closed bose-string theory. Requiring also that massless chiral fermions arise from the geometry/topology of coset space, we are left with the unique possibility: it implies D = 14 subcritical dimensions and certain isometry group.

the subgroups of symplectic groups which fix a non-zero vector of the underlying symplectic space are called emph{affine subgroups.}~the split extension group $a(4)cong 2^7{:}sp_6(2)$ is the affine subgroup of the symplectic group $sp_8(2)$ of index $255$‎. ‎in this paper‎, ‎we use the technique of the fischer-clifford matrices to construct the character table of the inertia group $2^7{:}o^{-}_...

The abelian and monoidal structure of the category smooth weight modules over a non-integrable affine vertex algebra rank greater than one is an interesting, difficult essentially wide open problem. Even conjectures are lacking. This work details tests such conjecture for $$L_{-\frac{3}{2}}(\mathfrak {sl}_3)$$ via logarithmic Kazhdan–Lusztig correspondence. We first investigate representation t...