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 ...

For a Hopf algebra B, we endow the Heisenberg double H(B^*) with the structure of a module algebra over the Drinfeld double D(B). Based on this property, we propose that H(B^*) is to be the ...

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 ...

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 ...

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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 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 ...

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 ...