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I think it has first been considered by A.A. Albert in $1948$, in connection with so-called Lie-admissible algebras. An algebra $(A,\cdot)$ is called Lie-admissible, if $[a,b]=a\cdot b-b\cdot a$ defin …

As already mentioned, an easy argument using the Levi decomposition shows that there are three distinct indecomposable non-solvable Lie algebras of dimension $5$. However, I think it is worth to poin …

Yes, the morhpisms have been described in detail in the paper "A seven-term exact sequence for the cohomology of a group extension" by Dekimpe, Hartl and Wauters: see http://arxiv.org/pdf/1103.4052.pd …

The mentioned result of Cohn has been further extended. Let us write $σ(G) = n$ whenever $G$ is the union of $n$ proper subgroups, but is not the union of any smaller number of proper sub- groups. Thu …

There is a Magma BKLC (Best Known Linear Codes, i.e., linear $[n,k,d]_q$-codes, which have the highest minimum weight among all known linear $[n, k,d]_q$-codes) database. It contains also generator ma …

Jean-Louis Loday, Bruno Vallette "Algebraic operads", Grundlehren Math. Wiss. 346, Springer, Heidelberg, 2012. This book also has a lot of information on nonassociative algebras. Many interesting non …

Here are some references (which are not mentioned in Resolutions of Lie algebras). First I can recommend the book of Charles A. Weibel, An Introduction to Homological Algebra. It answers your questio …

The following result is proved in Bourbaki's book on Lie algebras: Theorem (A converse to the First Whitehead Lemma). Any finite-dimensional Lie algebra over the field of characteristic zero such tha …

Kostant and Sullivan proved that the Euler characteristic of a compact complete affine manifolds must vanish, affirming the Chern conjecture in the complete case (Bull. AMS 81 (1975)). Benzecri proved …

Profinite groups were first called "Groups of Galois type", see J.P. Serre's book "Cohomologie Galoisienne" of $1964$. The term "profinite" comes from Serre (if I am not mistaken). Of course, some pro …

Yes, the first congruence was conjectured by Chowla and Cowles in $1980$ and proved by Y. Mimura in $1983$, see http://www.sciencedirect.com/science/article/pii/0022314X83900380. For $B_n$ the sequen …

They are the compact Lie algebras. Note that are two different definitions in the literature. One is that a compact Lie algebra is the Lie algebra of a compact Lie group. This includes tori, and the K …

I like the book of Ireland and Rosen "A classical Introduction to Modern Number Theory". There the Cubic and Biquadratic Reciprocity law are proved (and the Eisenstein Reciprocity law , the $m$-th pow …

Grothendieck expected the moduli spaces $\mathcal{M}_{g,n}$ over $\mathbb{Q}$ to be the basic examples of anabelian varieties (besides hyperbolic curves, which was proved by Mochizuki, even over numbe …

There is a paper of Martin Lustig on his webpage giving a positive answer to the conjugacy problem for the outer automorphism group of the free group $F_n$. On the other hand, there seems not to be a …