Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

A rigid Leibniz algebra with non-trivial HL^2 (1508.06877v7)

Published 27 Aug 2015 in math.KT and math.RA

Abstract: In this article, we generalize Richardson's example of a rigid Lie algebra with non-trivial $H2$ to the Leibniz setting. Namely, we consider the hemisemidirect product ${\mathfrak h}$ of a semidirect product Lie algebra $M_k\rtimes{\mathfrak g}$ of a simple Lie algebra ${\mathfrak g}$ with some non-trivial irreducible ${\mathfrak g}$-module $M_k$ with a non-trivial irreducible ${\mathfrak g}$-module $I_l$. Then for ${\mathfrak g}={\mathfrak s}{\mathfrak l}_2({\mathbb C})$, we take $M_k$ (resp. $I_l$) to be the standard irreducible ${\mathfrak s}{\mathfrak l}_2({\mathbb C})$-module of dimension $k+1$ (resp. $l+1$). Assume $\frac{k}{2}>5$ is an odd integer and $l>2$ is odd, then we show that the Leibniz algebra ${\mathfrak h}$ is geometrically rigid and has non-trivial $HL2$ with adjoint coefficients. We close the article with an appendix where we record further results on the question whether $H2({\mathfrak g},{\mathfrak g})=0$ implies $HL2({\mathfrak g},{\mathfrak g})=0$.

Summary

We haven't generated a summary for this paper yet.