Thus, one has the general statement that the tensor algebra of any Lie algebra is a Poisson algebra.
12.
The above universal property shows that the construction of the tensor algebra is " functorial " in nature.
13.
This approach was generalized by the theory of Analytic programming space ), through tensor algebra of the dual space.
14.
The tensor algebra is simply the disjoint union ( direct sum ?" ) of all tensor products of this vector space.
15.
The Signature is a homomorphism from the monoid of paths ( under concatenation ) into the grouplike elements of the free tensor algebra.
16.
For example the tensor algebra construction on a vector space as left adjoint to the functor on associative algebras that ignores the algebra structure.
17.
Cartesian tensors are as in tensor algebra, but Euclidean structure of and restriction of the basis brings some simplifications compared to the general theory.
18.
The tensor algebra is important because many other algebras arise as quotient algebras of " T " ( " V " ).
19.
A method of deriving the EM field transformations in an efficient way which also illustrates the unit of the electromagnetic field uses tensor algebra, given below.
20.
The construction of the symmetric algebra as a quotient of the tensor algebra is, as functors, a composition of the free algebra functor with this reflection.
