All Questions
8 questions with no upvoted or accepted answers
6
votes
0
answers
102
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Computer program for free restricted Lie polynomial
I am conducting numerical experiments involving the Gröbner–Shirshov Basis for restricted Lie algebras. At each step of the computation, I need to work with restricted Lie polynomials. Specifically, I ...
- 1,013
5
votes
0
answers
154
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One-parameter family of algebra structures: characterizing trivial deformation as adjoint 2-cocycle being a 2-coboundary
$\DeclareMathOperator\C{\mathbf{C}}$Motivation: this post discusses a simple criterion for a 1-parameter family of $n$-dimensional complex algebras to be a "trivial deformation", i.e., be ...
- 63.9k
4
votes
1
answer
241
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Regular nilpotents and minimal parabolic subalgebras in real semisimple Lie algebras
Let $\mathfrak{g}$ be a real semisimple Lie algebra. A subalgebra $\mathfrak{p}$ of $\mathfrak{g}$ is parabolic if its complexification is parabolic in $\mathfrak{g}_\mathbb{C}$, meaning it contains a ...
user126256
4
votes
0
answers
188
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Macdonald's notes on Kac Moody algebras
Macdonald had given some lectures on Kac-Moody algebras in 1983. The notes are typed here by Arun Ram. However, the website seems to be old and the notes are somewhat not readable because of the ...
- 820
2
votes
0
answers
145
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The "big bracket" in Lie bialgebras
I am looking for a well-written document such as a survey article or textbook that explores the subject of the "big bracket". This concept is briefly introduced in the appendix of Yvette ...
- 442
2
votes
0
answers
145
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Solvability and nilpotency for Banach algebras
Do we have topological counterparts of solvability and nilpotency, which are central concepts for (finite-dimensional) Lie algebras, for infinite dimensional Banach algebras with the commutator ...
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2
votes
0
answers
86
views
Kernel of some expressions in real Lie algebras
Let $\mathfrak{g}$ be a real Lie algebra and let $\mathfrak{g}=\mathfrak{k}\oplus\mathfrak{p}$ be a Cartan decomposition of $\mathfrak{g}$. Let $\mathfrak{a}$ be maximal abelian subalgebra of $\...
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1
vote
0
answers
60
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Reference for Gröbner-Shirshov algorithm in free restricted Lie algebras
I am searching for a reference on the Gröbner-Shirshov algorithm specifically for free restricted Lie algebras. I have already consulted the textbook by Bokut et al (Gröbner–Shirshov Bases Normal ...
- 1,013