1. CJM 2008 (vol 60 pp. 892)
|The Second Cohomology of Current Algebras of General Lie Algebras |
Let $A$ be a unital commutative associative algebra over a field of characteristic zero, $\k$ a Lie algebra, and $\zf$ a vector space, considered as a trivial module of the Lie algebra $\gf := A \otimes \kf$. In this paper, we give a description of the cohomology space $H^2(\gf,\zf)$ in terms of easily accessible data associated with $A$ and $\kf$. We also discuss the topological situation, where $A$ and $\kf$ are locally convex algebras.
Keywords:current algebra, Lie algebra cohomology, Lie algebra homology, invariant bilinear form, central extension
2. CJM 1998 (vol 50 pp. 210)
|Isomorphisms between generalized Cartan type $W$ Lie algebras in characteristic $0$ |
In this paper, we determine when two simple generalized Cartan type $W$ Lie algebras $W_d (A, T, \varphi)$ are isomorphic, and discuss the relationship between the Jacobian conjecture and the generalized Cartan type $W$ Lie algebras.
Keywords:Simple Lie algebras, the general Lie algebra, generalized Cartan type $W$ Lie algebras, isomorphism, Jacobian conjecture
Categories:17B40, 17B65, 17B56, 17B68