Exercise 6, § 4

Tag 011L, permanent. Cite it as [Bourbaki, Tag 011L].

Lie Groups and Lie Algebras, VIII, 232

Let A be a commutative ring, and let $\mathfrak{u}$ be the A-Lie algebra defined by the family of generators $\{x, y\}$ and the relations

[x,[x, y]] = 0,[y,[y,[y, x]]] = 0

Show that $\mathfrak{u}$ is a free A-module with basis

\{x, y,[x, y],[y,[x, y]]\}

Show that, when $A =k,\mathfrak{u}$ is isomorphic to the algebra $\mathfrak{a}_+/\mathfrak{n}$ corresponding to a root system of type $B_2$ .

Solution

No solution has been written yet.

Cited by

Nothing.

Nothing.