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Simple Lie algebras arising from Leavitt path algebras
Leavitt path algebra simple Lie algebra commutator
2011/9/9
Abstract: For a field K and directed graph E, we analyze those elements of the Leavitt path algebra L_K(E) which lie in the commutator subspace [L_K(E), L_K(E)]. This analysis allows us to give easily...
Classification of Simple Lie Algebras on a Lattice
Simple Lie Algebras Lattice Representation Theory Mathematical Physics
2011/9/1
Abstract: Let $\Lambda$ be a lattice of rank $n$. A Lie algebra on the lattice $\Lambda$ is a Lie algebra ${\cal L}=\oplus_{\lambda\in\Lambda}\,{\cal L}_{\lambda}$ such that $\dim\,{\cal L}_\lambda=1$...
Given an element P(X1, . . . ,Xd) of the free Lie K-algebra Ld, for any Lie algebra g we can consider the induced polynomial map P : gd → g. Assuming that K is an arbitrary field of characteristic 6= ...
Universal central extensions of twisted forms of split simple Lie algebras over rings
Universal central extensions Lie algebras
2010/11/23
We give sufficient conditions for the descent construction to be the universal central extension of a twisted form of a split simple Lie algebra over a ring. In particular, the universal central exten...