In mathematics, the tensor product of representations is a tensor product of vector spaces underlying representations together with the factor-wise group...

tensor product of v {\displaystyle v} and w {\displaystyle w} . An element of V ⊗ W {\displaystyle V\otimes W} is a tensor, and the tensor product of...

the tensor product and ρ 2 ( x ) {\displaystyle \rho _{2}(x)} acts on the second factor in the tensor product. In the context of representations of the...

isomorphism) exactly the tensor product of the irreducible representations of the factor groups. First, we note that the direct product G 1 × G 2 {\displaystyle...

_{2}(X)} . This product can be recognized as the coproduct on a coalgebra. In general, the tensor product of irreducible representations is not irreducible;...

_{2}:G\rightarrow GL(V_{2})} , then the tensor product of the representations would have the tensor product vector space V 1 ⊗ V 2 {\displaystyle V_{1}\otimes...

In graph theory, the tensor product G × H of graphs G and H is a graph such that the vertex set of G × H is the Cartesian product V(G) × V(H); and vertices...

representation of dimension 5 corresponding to the exceptional transitive embedding of A5 in A6. The tensor product of two representations of S n {\displaystyle...

learning, the term tensor informally refers to two different concepts (i) a way of organizing data and (ii) a multilinear (tensor) transformation. Data...

leads to the concept of a tensor field. In some areas, tensor fields are so ubiquitous that they are often simply called "tensors". Tullio Levi-Civita...

of R-algebras. Tensor products The tensor product of two R-algebras is also an R-algebra in a natural way. See tensor product of algebras for more details...

product, sometimes denoted by ⊗, is an operation on two matrices of arbitrary size resulting in a block matrix. It is a specialization of the tensor product...

In mathematics, the tensor product of two algebras over a commutative ring R is also an R-algebra. This gives the tensor product of algebras. When the...

ring) Tensor product of representations, a special case in representation theory Tensor product of fields, an operation on fields—unlike most tensor products...

representation that is an infinite tensor product of representations of p-adic groups, with specific enveloping algebra representations for the infinite prime(s)...

mathematics, specifically multilinear algebra, a dyadic or dyadic tensor is a second order tensor, written in a notation that fits in with vector algebra. There...

mathematics, the tensor representations of the general linear group are those that are obtained by taking finitely many tensor products of the fundamental...

decomposition of the tensor product of two representations of a group into a direct sum of irreducible representations. The term is often used in the context of two-dimensional...

morphisms. The category of linear representations of a group has a monoidal structure given by the tensor product of representations, which is an important ingredient...

obtained as a tensor product of two fundamental or antifundamental representations. For example, the MN-dimensional representation (M,N) of the group S...

particularly of compact Lie groups, to perform the explicit direct sum decomposition of the tensor product of two irreducible representations (i.e., a reducible...

Hall (2015, Proposition 4.18) about Lie algebra representations of group tensor product representations. The "traceless" property can be expressed as Sαβgαβ...

the set of equivalence classes of irreducible unitary representations of G. The analogue of the product of characters is the tensor product of representations...

Tensor networks or tensor network states are a class of variational wave functions used in the study of many-body quantum systems and fluids. Tensor networks...

category theory, a branch of mathematics, a symmetric monoidal category is a monoidal category (i.e. a category in which a "tensor product" ⊗ {\displaystyle \otimes...

dual representation. Modules of Hopf algebras do, however. Complex conjugate representation Tensor product of representations Kirillov Character Formula...

differential geometry, a tensor density or relative tensor is a generalization of the tensor field concept. A tensor density transforms as a tensor field when passing...

For example, V ⊗ V, the tensor product of V with itself, has a basis consisting of tensors of the form eij = ei ⊗ ej. Any tensor T in V ⊗ V can be written...

structure, from the tensor algebra. See the article on tensor algebras for a detailed treatment of the topic. The exterior product of multilinear forms...

allows for the construction of tensor products of representations, trivial representations, and dual representations. Hopf algebras occur naturally in...