Homological algebra and module theory constitute a vibrant area of contemporary mathematics, interweaving concepts from algebra, topology and geometry. At its core, homological algebra studies chain ...

1 School of Mathematics, Shanghai University of Finance and Economics, Shanghai, China. The category of left -comodule is denoted by. For more about modules and comodules, see [1] -[3] . (a1) is a ...

Algebra and calculus are essential branches of mathematics and for most students are the main areas of maths they have seen at high school. Algebra involves manipulating expressions and solving ...

Before you start, it may be helpful to read the guides on coordinates and graphs from Module 2 (M2) and Module 3 (M3). When two lines are perpendicular, the product of their gradients is 1. Lines A ...

Before reading this guide, you may find it helpful to read the guide on graphs from Module 7 (M7) and the guide on indices from Module 8 (M8). In Module 7 (M7) Graphs, you learned that simultaneous ...

Weak Hopf algebras were introduced by G. Böhm and K. Szlachányi as a generalization of usual Hopf algebras and groupoid algebras [1] [2] . A weak Hopf algebra is a vector space that has both algebra ...

We show that the full matrix algebra Mat_p(C) is a quantum commutative U-module algebra for U=U_q sl(2), a quantum sl(2) group at the 2p-th root of unity. Mat_p(C) decomposes into a direct sum of ...

Abstract: We give a path model for a level-zero extremal weight module over a quantum affine algebra. By using this result, we prove branching rules for an extremal weight module and a fundamental ...

There are more undocumented features which will be explained once the design matures. Fundamental principle of design is to construct Field algebra from an abelian Group algebra construction built on ...