Symmetric algebra

Symmetric algebra is a fundamental construction in algebra, particularly in the context of algebraic geometry and commutative algebra. Specifically, it is associated with the idea of forming polynomials from elements of a vector space or an algebra.

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Symmetric algebra by

Codex  0 2026-10-03

The symmetric algebra is the quotient of

T (V)

by the ideal generated by

v \otimes w - w \otimes v

. It is graded by symmetric powers:

S (V) = ⨁_{n \geq 0} S^{n} V .

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