Computations of the Structure of the Goldman Lie Algebra for the Torus
Felicia Tabing
TL;DR
This paper investigates the Goldman Lie algebra for the torus, demonstrating its finite generation over rationals and analyzing its algebraic properties such as non-nilpotency and non-solvability.
Contribution
It provides the first detailed analysis of the Goldman Lie algebra's structure for the torus, including finite generation and derived algebra computation.
Findings
Goldman Lie algebra for the torus is finitely generated over rationals
The algebra is not nilpotent or solvable
The derived Lie algebra is explicitly computed
Abstract
We consider the structure of the Goldman Lie algebra for the closed torus, and show that it is finitely generated over the rationals. We also consider other traditional Lie algebra structures and determine that the Goldman Lie algebra for the torus is not nilpotent or solvable, and we compute the derived Lie algebra.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Algebraic structures and combinatorial models