21 Übersetzungen
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Anwendungsbeispiele Englisch
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- The exterior algebra (as well as the symmetric algebra) inherits a bialgebra structure, and, indeed, a Hopf algebra structure, from the tensor algebra.
- This is done by taking the tangent space as a vector space, extending it to a tensor algebra, and then using an inner product on the vector space to define a Clifford algebra.
- Tensors equipped with their product operation form an algebra, called the tensor algebra.
- For example, the tensor algebra construction on a vector space is the left adjoint to the functor on associative algebras that ignores the algebra structure.
- In the category of (noncommutative) "R"-algebras, the coproduct is a quotient of the tensor algebra (see free product of associative algebras).
- The Wightman axioms can be rephrased in terms of a state called a Wightman functional on a Borchers algebra equal to the tensor algebra of a space of test functions.
- Other examples of bialgebras include the tensor algebra, which can be made into a bialgebra by adding the appropriate comultiplication and counit; these are worked out in detail in that article.
- There are other general examples, as well: it occurs in the theory of Lie algebras, where the tensor algebra of a Lie algebra forms a Poisson algebra; a detailed construction of how this comes about is given in the universal enveloping algebra article.
- This statement is an initial property of the tensor algebra since it expresses the fact that the pair [...] , where [...] is the inclusion map, is a universal morphism from the vector space [...] to the functor [...].
© dict.cc English-German dictionary 2024
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