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The symmetric algebra of a vector space is generated by powers

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#linear-algebra #polynomials #symmetric-algebra
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Definition of symmetric power of a linear represenation

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#representation-theory #functors #symmetric-algebra
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Proving Symmetric Difference of A and B

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#formal-proofs #symmetric-algebra
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$G$ is Lie group and $V$ is a representations of $G$,prove representations $V \otimes V \cong S^2(V) \oplus \Lambda^2(V)$

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#representation-theory #lie-groups #multilinear-algebra #exterior-algebra #symmetric-algebra
226
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What is the subspace of alternating (not antisymmetric) tensors?

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#multilinear-algebra #exterior-algebra #symmetric-algebra
20
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Sequence of monotonic transposition characterisation

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#group-theory #permutations #symmetric-groups #permutation-cycles #symmetric-algebra
277
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Symmetric square of the fundamental representation of $SU(2)$ is irreducible

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#group-theory #representation-theory #lie-groups #lie-algebras #symmetric-algebra
243
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Harish Chandra isomorphism:Invariant polynomial functions

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#linear-algebra #lie-algebras #weyl-group #symmetric-algebra
108
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Is Fock space a symmetric/exterior algebra?

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#abstract-algebra #exterior-algebra #quantum-field-theory #symmetric-algebra
75
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If $M$ is a cyclic $R$-module, then the tensor-algebra of $M$ is equal to the symmetric algebra of $M$, i.e. $\mathcal{T}(M) = \mathcal{S}(M)$

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#modules #tensors #symmetric-algebra
44
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Mixed symmetric algebra and applications to linear algebra?

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#linear-algebra #abstract-algebra #reference-request #exterior-algebra #symmetric-algebra
24
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Polynomial rings and symmetric algebras on the dual module are isomorphic

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#polynomials #free-modules #symmetric-algebra
79
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Symmetric algebra and exact sequences

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#ring-theory #modules #exact-sequence #symmetric-algebra
654
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Determinant of exterior power and symmetric power

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#abstract-algebra #determinant #multilinear-algebra #exterior-algebra #symmetric-algebra
116
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How does the nth Symmetric Power result from the quotient of the group of rank N tensors?

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#abstract-algebra #quotient-group #symmetric-algebra

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