Let $E$ be a vector space. I'm interested in examples of left ideals in exterior algebra $ \Lambda E$ that aren't right ideals.
2026-03-26 01:02:10.1774486930
Left ideals in exterior algebra $\Lambda E$ that aren't right
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being encouraged by Georges Elencwajg :)
the simplest example I can come up with is $E$ with basis $a,b,c,d$ and the left ideal generated by $a+bc$; one easily checks that $(a+bc)d\notin I$. How to find it: $\bigwedge E$ is noncommutative, but it is graded-commutative. Ideals generated by $\mathbb Z/2\mathbb Z$-homogeneous elements are thus going to be both-sided. A simple inhomogeneous element which works is $a+bc$.