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Results tagged with lie-algebras
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user 10881
Lie algebras are algebraic structures which were introduced to study the concept of infinitesimal transformations. The term "Lie algebra" (after Sophus Lie) was introduced by Hermann Weyl in the 1930s. In older texts, the name "infinitesimal group" is used. Related mathematical concepts include Lie groups and differentiable manifolds.
3
votes
Breaking up the free Lie algebra into GL irreps
Here is the result, computed using sage:
sage: def lie(n):
....: p = SymmetricFunctions(QQ).p()
....: return p.sum_of_terms((Partition([d for j in range(ZZ(n / d))]),
....: …
- 3,597
7
votes
A mysterious Heisenberg algebra identity from Sylvester, 1867
This can be interpreted cleanly using the notion of Pre-Lie algebra.
Indeed, vector fields on an affine space form a Pre-Lie algebra. To prove the desired identity, it is enough to consider the free …
- 3,597
5
votes
Ternary "Lie structure"
The proper setting is the theory of operads, which allows to deal with any number of generators at a single stroke.
The Lie operad is the sub-operad of the associative operad generated by 12-21.
Th …
- 3,597
3
votes
Compute formal character of semisimple Lie algebras.
You can use sage for this (and for many other things)
See the following manual page:
The Weyl character ring
- 3,597