Applying the density theorem for derivations to range inclusion problems
The problem of when derivations (and their powers) have the range in the Jacobson radical is considered. The proofs are based on the density theorem for derivations.
Symmetric algebras and Yang-Baxter equation
Let be an open subset of the complex plane, and let denote a finite-dimensional complex simple Lie algebra. and investigated non-degenerate meromorphic functions from into which are solutions of the classical Yang-Baxter equation [Funct. Anal. Appl. 16, 159-180 (1983; Zbl 0504.22016)]. They found that (up to equivalence) the solutions depend only on the difference of the two variables and that their set of poles forms a discrete (additive) subgroup of the complex numbers (of rank at...
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