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The exterior algebra is the direct sum of the -th exterior powers of , and this makes the exterior algebra a graded algebra. The exterior algebra is universal in the sense that every equation that relates elements of V {\displaystyle V} in the exterior algebra is also valid in every associative algebra that contains V {\displaystyle V} and in ...
In mathematics and classical mechanics, the Poisson bracket is an important binary operation in Hamiltonian mechanics, ... (i.e., its exterior derivative ...
The exterior derivative is natural in the technical sense: if f : M → N is a smooth map and Ω k is the contravariant smooth functor that assigns to each manifold the space of k-forms on the manifold, then the following diagram commutes
In architecture, a corbel is a structural piece of stone, wood or metal jutting from a wall to carry a superincumbent weight, [1] a type of bracket. [2] A corbel is a solid piece of material in the wall, whereas a console is a piece applied to the structure. A piece of timber projecting in the same way was called a "tassel" or a "bragger" in ...
Let be a vector space over a field equipped with a linear mapping : from to the exterior product of with itself. It is possible to extend uniquely to a graded derivation (this means that, for any , which are homogeneous elements, () = + ()) of degree 1 on the exterior algebra of :
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