Symmetric Algebra
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In mathematics, the symmetric algebra S(V) (also denoted Sym(V)) on a vector space V over a field (mathematics)|field K is the Free object|free commutative unital algebra|unital associative algebra over K containing V. It corresponds to polynomials with indeterminates in V, without choosing coordinates. The dual, S(V*) corresponds to polynomials on V. It should not be confused with symmetric tensors in V. A Frobenius algebra whose bilinear form is symmetric bilinear form|symmetric is also called a symmetric algebra, but is not discussed here.
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