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Results tagged with ra.rings-and-algebras
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user 766
Non-commutative rings and algebras, non-associative algebras, universal algebra and lattice theory, linear algebra, semigroups. For questions specific to commutative algebra (that is, rings that are assumed both associative and commutative), rather use the tag ac.commutative-algebra.
21
votes
4
answers
1k
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Can one show the equivalence of the abstract and classical Jordan decompositions for simple ...
The following fact is basic in the theory of complex Lie algebras:
Theorem. Let ${\mathfrak g} \subset {\mathfrak gl}_n({\bf C})$ be a simple Lie algebra, and let $x \in {\mathfrak g}$. Let $x = …
- 114k
17
votes
0
answers
1k
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Relations in a certain Lie algebra
Let ${\mathfrak g}$ be the (real) Lie algebra generated by infinitely many generators $D_i, E_i$ with $i=1,2,3,\dots$ subject to the following relations for any natural numbers $i,j$:
\begin{gather*}
…
- 114k
25
votes
2
answers
2k
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What is the name of this relative semidirect product of groups?
We have two well known definitions of the semidirect product $N \rtimes H$ of groups:
(Internal semidirect product) We write $G = N \rtimes H$ if $N$ is a normal subgroup of $G$, $H$ is another subg …
- 114k
32
votes
1
answer
2k
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Is this formal noncommutative power series identity known?
I recently discovered the following cute formal noncommutative power series identity: if $(x_i)_{i \in I}$ is some finite collection of noncommuting variables, then the formal power series
$$ 1 + \sum …
- 114k