In mathematics, the exterior algebra or Grassmann algebra of a vector space V {\displaystyle V} is an associative algebra that contains V , {\displaystyle...

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...

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...

differential forms by the interior product. The algebra of differential forms along with the exterior derivative defined on it is preserved by the pullback...

tensor algebra is important because many other algebras arise as quotient algebras of T(V). These include the exterior algebra, the symmetric algebra, Clifford...

their manipulation is carried out using exterior algebra. Following Grassmann, developments in multilinear algebra were made by Victor Schlegel in 1872 with...

symmetric algebra and an exterior algebra Weyl algebra, a quantum deformation of the symmetric algebra by a symplectic form Clifford algebra, a quantum...

"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...

enveloping algebra of a Lie algebra is the unital associative algebra whose representations correspond precisely to the representations of that Lie algebra. Universal...

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...

(anti)derivation on the exterior algebra of differential forms on a smooth manifold. The interior product, named in opposition to the exterior product, should...

A non-associative algebra (or distributive algebra) is an algebra over a field where the binary multiplication operation is not assumed to be associative...

Multilinear algebra Tensor Classical treatment of tensors Component-free treatment of tensors Gamas's Theorem Outer product Tensor algebra Exterior algebra Symmetric...

alternating algebra. The exterior algebra is an alternating algebra. The cohomology ring of a topological space is an alternating algebra. The algebra formed...

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...

In mathematics, a Hopf algebra, named after Heinz Hopf, is a structure that is simultaneously an (unital associative) algebra and a (counital coassociative)...

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...

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...

{\displaystyle x=4} ). Algebra over a set Algebra tile Algebraic combinatorics C*-algebra Composition algebra Computer algebra Exterior algebra F-algebra F-coalgebra...

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...

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...

In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are sets with specific operations...

bialgebras. Examples of coalgebras include the tensor algebra, the exterior algebra, Hopf algebras and Lie bialgebras. Unlike the polynomial case above...

algebra Differential graded Lie algebra Exterior algebra F-algebra Filtered algebra Flexible algebra Freudenthal algebra Functional-theoretic algebra...

commutative algebra is a supercommutative algebra if given the trivial gradation (i.e. all elements are even). Grassmann algebras (also known as exterior algebras)...

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...

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...

matrixPages displaying short descriptions of redirect targets Exterior algebra – Algebra of exterior/ wedge products Levi-Civita symbol – Antisymmetric permutation...

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...

not in this nonnegative-graded exterior algebra, but in the graded algebra of derivations over the exterior algebra; the 78-dimensional e 6 {\displaystyle...