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Results tagged with lie-algebras
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user 3473
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.
8
votes
What is Pressley and Segal's "basic inner product" for compact simple Lie algebras of types ...
Section 4 of
Gawȩdzki, Krzysztof; Reis, Nuno, Basic gerbe over non-simply connected compact groups, J. Geom. Phys. 50, No. 1-4, 28-55 (2004). ZBL1067.22009.
lists, in an absolutely concrete way, the s …
- 4,519
4
votes
2-cocycle on LSU(2)
I second André's comment that one cannot expect interesting, smooth 2-cocycles $\omega: LG \times LG \to S^1$. The situation for Lie groups is simply different to the one for Lie algebras: central Lie …
- 4,519
4
votes
Accepted
Is the restriction of the Cartan 3-form on conjugacy classes exact?
Yes, it is exact, and there is in fact a canonical 2-form on each conjugacy class whose derivative is your $\Omega$. This was an important observation when studying D-branes in WZW models, see, e.g. h …
- 4,519