tensor algebra sentence in Hindi
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- This universal property follows from the tensor algebra as a natural transformation.
- This distinction is developed in greater detail in the article on tensor algebras.
- Additional discussion of this point can be found in the tensor algebra article.
- Here juxtaposition is symmetric respectively antisymmetric multiplication in the symmetric and antisymmetric tensor algebra.
- The universal property can thus be seen as being inherited from the tensor algebra.
- Thus, these two are consistency conditions for the Lie bracket on the tensor algebra.
- The construction proceeds by first building the tensor algebra of the underlying vector space of the Lie algebra.
- The monomials of these generators then generate the tensor algebra, on which the quotienting may be performed.
- The result of the lifting is that the tensor algebra of a Lie algebra is a Poisson algebra.
- The construction generalizes in straightforward manner to the tensor algebra of any " commutative " ring.
- Thus, one has the general statement that the tensor algebra of any Lie algebra is a Poisson algebra.
- The above universal property shows that the construction of the tensor algebra is " functorial " in nature.
- This approach was generalized by the theory of Analytic programming space ), through tensor algebra of the dual space.
- The tensor algebra is simply the disjoint union ( direct sum ?" ) of all tensor products of this vector space.
- The Signature is a homomorphism from the monoid of paths ( under concatenation ) into the grouplike elements of the free tensor algebra.
- For example the tensor algebra construction on a vector space as left adjoint to the functor on associative algebras that ignores the algebra structure.
- Cartesian tensors are as in tensor algebra, but Euclidean structure of and restriction of the basis brings some simplifications compared to the general theory.
- The tensor algebra is important because many other algebras arise as quotient algebras of " T " ( " V " ).
- 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.
- 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.
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