Tensor, Exterior and Symmetric Algebras
نویسنده
چکیده
3 The Exterior Algebra 6 3.1 Dimension of the Exterior Powers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.2 Bilinear Forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.3 Other Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.3.1 The determinant formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
منابع مشابه
Tensor Algebras, Symmetric Algebras and Exterior Algebras
We begin by defining tensor products of vector spaces over a field and then we investigate some basic properties of these tensors, in particular the existence of bases and duality. After this, we investigate special kinds of tensors, namely, symmetric tensors and skew-symmetric tensors. Tensor products of modules over a commutative ring with identity will be discussed very briefly. They show up...
متن کاملA few classical results on tensor, symmetric and exterior powers
0.1. Version . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 0.2. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 0.3. Basic conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 0.4. Tensor products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 0.5. Tensor powers of k-modules . . . . . . . . . . . ...
متن کاملArens-irregularity of tensor product of Banach algebras
We introduce Banach algebras arising from tensor norms. By these Banach algebras we make Arensregular Banach algebras such that tensor product becomes irregular, where is tensor norm. Weillustrate injective tensor product, does not preserve bounded approximate identity and it is notalgebra norm.
متن کاملOn p-minimal homological models of twisted tensor products of elementary complexes localised over a prime
In this paper, working over Z(p) and using algebra perturbation results from [18], p-minimal homological models of twisted tensor products (TTPs) of Cartan’s elementary complexes are obtained. Moreover, making use of the notion of indecomposability of a TTP, we deduce that a homological model of a indecomposable p-minimal TTP of length ` (` ≥ 2) of exterior and divided power algebras is a tenso...
متن کاملTensor Product of Endo-permutation Modules
In this paper, we study some properties of the exterior tensor product on the category of modules. For this, we prove that the exterior tensor product of two permutation, endo-permutation, endo-trivial and endo-monomial modules are still permutation, endo-permutation endotrivial and endo-monomial modules respectively. Also, we prove that the cap of an exterior tensor product of two modules equa...
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تاریخ انتشار 2006