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Results tagged with lie-algebras
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user 750
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.
6
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Non-free projective modules for a Universal Enveloping Algebra?
Let g be a finite dimensional Lie algebra over k, and let U be its universal enveloping Lie algebra. Is there a left module M of U which is projective but not free? That is, is the Quillen-Suslin th …
- 13k
1
vote
Longest Element of an Affine Weyl Group
I don't know very much about this, but I have heard that in the theory of 'buildings' (nice simplicial complexes on which Coexeter groups act), the affine Weyl groups act naturally on 'twin buildings' …
- 13k
8
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Relation between Lie Algebra Cohomology and Number of Relations of a Cyclic Module?
Let $\mathfrak{g}$ be a finite dimensional Lie algebra over $k$, let $U$ be its enveloping algebra, and let $M$ be a $\mathfrak{g}$-module (not necessarily finite dimensional). Call the invariant dim …
- 13k
4
votes
Accepted
Matrices into path algebras
There's a slightly different equivalence that is also useful. Consider the quiver with n elements, and an arrow E_i from i to i+1 and another F_i from i+1 to i for all i. The relations are then that …
- 13k