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Tag Archives: tensor products
Polynomials and Representations XXXIX
Some Invariant Theory We continue the previous discussion. Recall that for we have a equivariant map which induces an isomorphism between the unique copies of in both spaces. The kernel Q of this map is spanned by for various fillings T with shape and entries … Continue reading
Polynomials and Representations XXXVII
Notations and Recollections For a partition , one takes its Young diagram comprising of boxes. A filling is given by a function for some positive integer m. When m=d, we will require the filling to be bijective, i.e. T contains {1,…,d} and each element occurs exactly … Continue reading
Modular Representation Theory (III)
Let’s work out some explicit examples of modular characters. First, we have a summary of the main results. Let be the modular characters of the simple k[G]modules; they form a basis of Let be those of the projective indecomposable k[G]modules; they form a basis … Continue reading
Tensor Product over Noncommutative Rings
Following the earlier article on tensor products of vector spaces, we will now look at tensor products of modules over a ring R, not necessarily commutative. It turns out we have to distinguish between left and right modules now. Indeed recall … Continue reading
Posted in Notes
Tagged bimodules, hom functor, leftexact, modules, rightexact, tensor products
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Tensor Product and Linear Algebra
Tensor products can be rather intimidating for firsttimers, so we’ll start with the simplest case: that of vector spaces over a field K. Suppose V and W are finitedimensional vector spaces over K, with bases and respectively. Then the tensor product is the vector … Continue reading
Posted in Notes
Tagged bilinear maps, duals, linear algebra, tensor algebra, tensor products, universal properties
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