exact after tensoring, a pure submodule defines a short exact sequence (known as a pure exact sequence) that remains exact after tensoring with any module...
5 KB (700 words) - 01:12, 6 May 2024
\mathbb {Q} } is a flat Z {\displaystyle \mathbb {Z} } -module. Therefore, tensoring with Q {\displaystyle \mathbb {Q} } as a Z {\displaystyle \mathbb {Z}...
13 KB (2,404 words) - 19:02, 4 March 2024
⊗ A {\displaystyle B\otimes A} , the distinction between tensoring on the left and tensoring on the right becomes immaterial, so every right closed braided...
7 KB (1,167 words) - 18:33, 17 September 2023
= Spin(3) (as it sits inside the 3-dimensional Clifford algebra) have tensored to produce a 4-dimensional representation. The 4-dimensional representation...
7 KB (1,095 words) - 20:31, 12 September 2023
It captures the algebraic essence of tensoring, without making any specific reference to what is being tensored. Thus, all tensor products can be expressed...
50 KB (8,651 words) - 19:03, 15 August 2024
Chow group of cycles on X of dimension d modulo rational equivalence, tensored with the rational numbers. In case X is defined over the complex numbers...
18 KB (2,779 words) - 15:00, 8 July 2024
null-vector. If ξ {\displaystyle \xi } is a CP1 projective vector, it can be tensored with its Hermitian conjugate to produce a 2 × 2 {\displaystyle 2\times...
65 KB (9,740 words) - 02:08, 28 September 2024
saying the manifold is complex (which is what the chart definition says). Tensoring the tangent bundle with the complex numbers we get the complexified tangent...
10 KB (1,311 words) - 18:37, 9 September 2024
O ( D ) {\displaystyle {\mathcal {O}}(D)} is locally free, and hence tensoring that sequence by O ( D ) {\displaystyle {\mathcal {O}}(D)} yields another...
40 KB (6,609 words) - 18:59, 14 April 2023
representation. Another (n − 1)-dimensional irreducible representation is found by tensoring with the sign representation. An exterior power Λ k V {\displaystyle \Lambda...
20 KB (2,840 words) - 17:18, 21 January 2024
connected topological spaces with homotopy groups and singular homology groups tensored with the rational numbers, ignoring torsion elements and simplifying certain...
23 KB (1,897 words) - 01:55, 14 September 2024
summands of free modules. Flat modules are defined by the property that tensoring with them preserves exact sequences. Torsion-free modules form an even...
11 KB (1,808 words) - 16:43, 26 May 2024
algebra becomes a matrix algebra by extending scalars (equivalently, tensoring with a field extension), i.e. for a suitable field extension K of F, A...
10 KB (1,532 words) - 15:42, 21 February 2024
explicitly "complexified" to couple to electromagnetism. This is done by "tensoring in" an additional factor of the complex plane C {\displaystyle \mathbb...
35 KB (5,729 words) - 09:27, 17 June 2024
the natural map from the tensor product C ⊗ A to B ⊗ A is injective. Tensoring an abelian group A with Q (or any divisible group) kills torsion. That...
7 KB (911 words) - 21:28, 31 July 2024
also be called a pseudo-volume form, due to the additional sign twist (tensoring with the sign bundle). The volume element is a pseudotensor density according...
6 KB (1,032 words) - 06:55, 8 October 2024
anomaly, but may also refer to a mixture of two different gauge groups tensored together, like the SU(2) and the U(1) of the Standard Model. The anomaly...
2 KB (221 words) - 11:47, 21 July 2022
f(x)\otimes g(y)\end{cases}}} The construction has a consequence that tensoring is a functor: each right R-module M determines the functor M ⊗ R − : R...
48 KB (8,467 words) - 22:58, 6 April 2024
generally a complex number. This explains why the singular cohomology must be tensored to C, and from this point of view, C can be said to contain all the periods...
16 KB (2,317 words) - 18:04, 2 October 2024
a wide variety of different characterizations. A first point is that tensoring high powers of an ample line bundle with any coherent sheaf whatsoever...
39 KB (6,685 words) - 11:15, 9 October 2024
Mérida: Junta de Extremadura. pp. 1–4. "Tiene 26 años, 452 metros y 28 tensores". Hoy. 31 October 2010. Gilgado, Antonio (17 April 2017). "El radar del...
3 KB (194 words) - 14:15, 17 February 2024
K_{-p-q}(X).} As in topology, the spectral sequence degenerates after tensoring with the rationals. For arbitrary schemes of finite type over a field...
16 KB (2,285 words) - 19:58, 29 December 2023
manifold (M,ω) are naturally isomorphic to the ordinary cohomology of M, tensored by a suitable Novikov ring associated the group of covering transformations...
36 KB (4,649 words) - 00:59, 4 June 2024
Composing these isomorphisms yields two rational vector spaces which, after tensoring with C {\displaystyle \mathbb {C} } become isomorphic. Choosing bases...
26 KB (4,378 words) - 08:13, 20 September 2023
by all definitions of tensor products, irrespective of the spaces being tensored: this implies that any space with a tensor product is a symmetric monoidal...
12 KB (2,141 words) - 20:53, 17 April 2024
groups: 0 → A → B → C → 0 {\displaystyle 0\to A\to B\to C\to 0} Then tensoring with the rational numbers Q {\displaystyle \mathbb {Q} } implies the following...
24 KB (4,178 words) - 21:35, 19 July 2024
complex projective variety X, the Hodge conjecture predicts the image (tensored with the rationals Q) of the cycle map from the Chow groups to singular...
26 KB (4,195 words) - 07:43, 15 October 2024
labelled by extended Dynkin diagrams of type A, D and E; the rules for tensoring with the two-dimensional vector representation are given graphically by...
35 KB (3,977 words) - 15:35, 16 May 2024
{\mathcal {O}}(b).} As taking the projective bundle is invariant under tensoring by a line bundle, the ruled surface associated to E = O ( a ) ⊕ O ( b...
10 KB (1,693 words) - 12:07, 26 July 2024
{\displaystyle c_{1}(L)F=F-L^{-1}\otimes F.} It is additive on G since tensoring with a line bundle is exact. One also has: c 1 ( L 1 ) c 1 ( L 2 ) = c...
18 KB (3,298 words) - 13:08, 13 June 2024