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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeAug 18th 2010
   • (edited Aug 18th 2010)
   • PermaLink
   Author: Urs
   Format: MarkdownItexHave been polishing and expanding the first part of [[invariant polynomial]].

   Have been polishing and expanding the first part of invariant polynomial.

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeSep 19th 2010
   • PermaLink
   Author: Urs
   Format: MarkdownItexspelled out in hopefully pedagogical detail at [[invariant polynomial]] in the section <a href="http://ncatlab.org/nlab/show/invariant+polynomial#OnLieAlgebras">On Lie algebras</a> the proof that the definition given there (closed elements in shifted generators inthe Weil algebra) is equivalent to the traditional one

   spelled out in hopefully pedagogical detail at invariant polynomial in the section On Lie algebras the proof that the definition given there (closed elements in shifted generators inthe Weil algebra) is equivalent to the traditional one

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeJun 26th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexAt [[invariant polynomial]] had been missing a definition of the notion of equivalence of invariant polynomials on $L_\infty$-algebras that are not Lie algebras (where the notion does not play much of a role). I have added that into the Definition-section and then started adding to the Examples- and Properties-section a discusison on how this produces the expected behaviour that for $$ b^{n-1} \mathbb{R} \to \mathfrak{g}_\mu \to \mathfrak{g} $$ a shifted central extension of $L_\infty$-algebras induced from a transgressive cocycle $\mu : \mathfrak{g} \to b^n \mathbb{R}$ transgressing to $\langle-\rangle_\mu$, the invariant polynomials of $\mathfrak{g}_\mu$ are generated from the generators of those of $\mathfrak{g}$ except $\langle - \rangle_\mu$.

   At invariant polynomial had been missing a definition of the notion of equivalence of invariant polynomials on $L_\infty$-algebras that are not Lie algebras (where the notion does not play much of a role). I have added that into the Definition-section and then started adding to the Examples- and Properties-section a discusison on how this produces the expected behaviour that for

   $$b^{n-1} \mathbb{R} \to \mathfrak{g}_\mu \to \mathfrak{g}$$

   a shifted central extension of $L_\infty$-algebras induced from a transgressive cocycle $\mu : \mathfrak{g} \to b^n \mathbb{R}$ transgressing to $\langle-\rangle_\mu$, the invariant polynomials of $\mathfrak{g}_\mu$ are generated from the generators of those of $\mathfrak{g}$ except $\langle - \rangle_\mu$.

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeJun 30th 2011
   • (edited Jun 30th 2011)
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded in a new subsection [on reductive Lie algebras](http://ncatlab.org/nlab/show/invariant+polynomial#OnReductiveLieAlg) the statement that the invariant polynomials there form a free graded algebra on the indecomposables

   added in a new subsection on reductive Lie algebras the statement that the invariant polynomials there form a free graded algebra on the indecomposables

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeAug 28th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to the original references by Weil, Cartan and Chern (same original references that are now at _[[Chern-Weil homomorphism]]_) <a href="https://ncatlab.org/nlab/revision/diff/invariant+polynomial/37">diff</a>, <a href="https://ncatlab.org/nlab/revision/invariant+polynomial/37">v37</a>, <a href="https://ncatlab.org/nlab/show/invariant+polynomial">current</a>

   added pointer to the original references by Weil, Cartan and Chern (same original references that are now at Chern-Weil homomorphism)

   diff, v37, current