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Peirce Decomposition

Let A be a finite-dimensional power-associative algebra, then A is the vector space direct sum

A=A_(11)+A_(10)+A_(01)+A_(00),

where A_(ij), with i,j=0,1 is the subspace of A defined by

A_(ij)={x_(ij):ex_(ij)=ix_(ij),x_(ij)e=jx_(ij)}

for i,j=0,1, where e is an idempotent.

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References

Schafer, R. D. "The Peirce Decomposition." §3.2 in An Introduction to Nonassociative Algebras. New York: Dover, pp. 32-37, 1996.

Referenced on Wolfram|Alpha

Peirce Decomposition

Cite this as:

Weisstein, Eric W. "Peirce Decomposition." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PeirceDecomposition.html

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