In mathematics, the exterior algebra or Grassmann algebra of a vector space V {\displaystyle V} is an associative algebra that contains V , {\displaystyle...
76 KB (12,096 words) - 15:19, 19 August 2024
related exterior algebra. In 1878, William Kingdon Clifford greatly expanded on Grassmann's work to form what are now usually called Clifford algebras in his...
93 KB (13,918 words) - 12:02, 31 August 2024
Clifford algebras are closely related to exterior algebras. Indeed, if Q = 0 then the Clifford algebra Cl(V, Q) is just the exterior algebra ⋀V. Whenever...
64 KB (9,171 words) - 11:01, 7 August 2024
Differential form (redirect from Exterior differential form)
differential forms by the interior product. The algebra of differential forms along with the exterior derivative defined on it is preserved by the pullback...
66 KB (9,950 words) - 14:18, 10 February 2024
tensor algebra is important because many other algebras arise as quotient algebras of T(V). These include the exterior algebra, the symmetric algebra, Clifford...
23 KB (4,160 words) - 15:09, 12 January 2024
their manipulation is carried out using exterior algebra. Following Grassmann, developments in multilinear algebra were made by Victor Schlegel in 1872 with...
6 KB (661 words) - 02:59, 5 March 2024
symmetric algebra and an exterior algebra Weyl algebra, a quantum deformation of the symmetric algebra by a symplectic form Clifford algebra, a quantum...
13 KB (2,034 words) - 13:17, 31 January 2024
Spinor (section Exterior algebra construction)
"square roots" of sections of vector bundles – in the case of the exterior algebra bundle of the cotangent bundle, they thus become "square roots" of...
72 KB (9,924 words) - 08:41, 19 August 2024
enveloping algebra of a Lie algebra is the unital associative algebra whose representations correspond precisely to the representations of that Lie algebra. Universal...
52 KB (9,256 words) - 15:30, 31 August 2024
Multivector (category Multilinear algebra)
multilinear algebra, a multivector, sometimes called Clifford number or multor, is an element of the exterior algebra Λ(V) of a vector space V. This algebra is...
32 KB (4,838 words) - 22:45, 17 September 2023
Interior product (category Multilinear algebra)
(anti)derivation on the exterior algebra of differential forms on a smooth manifold. The interior product, named in opposition to the exterior product, should...
8 KB (1,586 words) - 00:01, 23 August 2024
A non-associative algebra (or distributive algebra) is an algebra over a field where the binary multiplication operation is not assumed to be associative...
25 KB (2,964 words) - 22:33, 1 September 2024
Multilinear algebra Tensor Classical treatment of tensors Component-free treatment of tensors Gamas's Theorem Outer product Tensor algebra Exterior algebra Symmetric...
5 KB (377 words) - 12:12, 30 October 2023
alternating algebra. The exterior algebra is an alternating algebra. The cohomology ring of a topological space is an alternating algebra. The algebra formed...
2 KB (155 words) - 19:15, 24 May 2024
the Hodge star operator or Hodge star is a linear map defined on the exterior algebra of a finite-dimensional oriented vector space endowed with a nondegenerate...
42 KB (6,824 words) - 21:45, 23 June 2024
In mathematics, a Hopf algebra, named after Heinz Hopf, is a structure that is simultaneously an (unital associative) algebra and a (counital coassociative)...
35 KB (4,397 words) - 17:50, 19 August 2024
Cross product (section Lie algebra)
a natural geometric interpretation of the cross product. In exterior algebra the exterior product of two vectors is a bivector. A bivector is an oriented...
75 KB (11,475 words) - 16:24, 26 July 2024
äußeres Produkt “outer product”), the key operation of an algebra now called exterior algebra. (One should keep in mind that in Grassmann's day, the only...
28 KB (3,197 words) - 07:38, 20 August 2024
{\displaystyle x=4} ). Algebra over a set Algebra tile Algebraic combinatorics C*-algebra Composition algebra Computer algebra Exterior algebra F-algebra F-coalgebra...
124 KB (12,662 words) - 16:47, 4 September 2024
Koszul duality (category Algebras)
a duality between the derived category of a symmetric algebra and that of an exterior algebra. The importance of the notion rests on the suspicion that...
8 KB (1,258 words) - 07:53, 21 May 2024
Bivector (category Geometric algebra)
In mathematics, a bivector or 2-vector is a quantity in exterior algebra or geometric algebra that extends the idea of scalars and vectors. Considering...
67 KB (9,905 words) - 13:15, 29 August 2024
In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are sets with specific operations...
32 KB (4,185 words) - 14:05, 4 June 2024
Coalgebra (redirect from Co-algebra)
bialgebras. Examples of coalgebras include the tensor algebra, the exterior algebra, Hopf algebras and Lie bialgebras. Unlike the polynomial case above...
20 KB (2,899 words) - 20:34, 13 May 2024
algebra Differential graded Lie algebra Exterior algebra F-algebra Filtered algebra Flexible algebra Freudenthal algebra Functional-theoretic algebra...
2 KB (226 words) - 16:33, 17 January 2024
commutative algebra is a supercommutative algebra if given the trivial gradation (i.e. all elements are even). Grassmann algebras (also known as exterior algebras)...
2 KB (322 words) - 19:35, 24 May 2024
Graded ring (redirect from Graded algebra)
In mathematics, in particular abstract algebra, a graded ring is a ring such that the underlying additive group is a direct sum of abelian groups R i...
16 KB (2,821 words) - 20:02, 17 August 2024
supernumber), is an element of the exterior algebra of a complex vector space. The special case of a 1-dimensional algebra is known as a dual number. Grassmann...
22 KB (3,855 words) - 14:49, 4 August 2024
matrixPages displaying short descriptions of redirect targets Exterior algebra – Algebra of exterior/ wedge products Levi-Civita symbol – Antisymmetric permutation...
5 KB (835 words) - 08:04, 2 July 2024
mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables...
75 KB (9,506 words) - 17:24, 21 June 2024
E8 (mathematics) (redirect from E8 Lie algebra)
not in this nonnegative-graded exterior algebra, but in the graded algebra of derivations over the exterior algebra; the 78-dimensional e 6 {\displaystyle...
46 KB (6,107 words) - 13:33, 2 September 2024