Exterior isoclinism gives an alternative classification method for finite Lie algebras and crossed modules. In this paper, we define the notions of exterior Also, generalize these n-th dimension.

We revisit the derivation of Knizhnik-Zamolodchikov equations in case nonsemisimple categories modules a superalgebra generic affne level and representations parameters. A proof existence asymptotic solutions their properties for $gl(1|1)$ gives basis associator which satisfy braided tensor requirements. Braided category structure $U_h(gl(1|1))$ quantum algebra calculated, product ring is shown...

We define a cotriple (co)homology of crossed modules with coefficients in a π1-module. We prove its general properties, including the connection with the existing cotriple theories on crossed modules. We establish the relationship with the (co)homology of the classifying space of a crossed module and with the cohomology of groups with operators. An example and an application are given.