Cohomology of Jordan triples via Lie algebras
Cho-Ho Chu, Bernard Russo
TL;DR
This paper introduces a cohomology theory for Jordan triples using TKK Lie algebras, allowing the transfer of Lie cohomological results to Jordan triples, with initial findings on von Neumann algebras.
Contribution
It develops a new cohomology framework for Jordan triples via Lie algebra methods, extending to infinite-dimensional cases and applying to von Neumann algebras.
Findings
Established cohomology theory for Jordan triples.
Connected Jordan triple cohomology with Lie algebra cohomology.
Obtained preliminary results for von Neumann algebras.
Abstract
We develop a cohomology theory for Jordan triples, including the infinite dimensional ones, by means of the cohomology of TKK Lie algebras. This enables us to apply Lie cohomological results to the setting of Jordan triples. Some preliminary results for von Neumann algebras are obtained.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology